Document [original]

Disaster recovery planning of transportation networks:

Problem structuring and decision attributes

vorgelegt von

M.Sc.

Milad Zamanifar

an der Fakultät VI — Planen Bauen Umwelt

der Technischen Universität Berlin

zur Erlangung des akademischen Grades

Doktor der Ingenieurwissenschaften

- Dr.-Ing. -

genehmigte Dissertation

Promotionsausschuss:

Vorsitzender: Univ.-Prof. Dr.-Ing. Wolfgang Huhnt

Gutachter: Univ.-Prof. Dr. Bryan T. Adey

Gutachter: Univ.-Prof. Dr.-Ing. Timo Hartmann

Gutachter: Univ.-Prof. Dr. Pingbo Tang

Tag der wissenschaftlichen Aussprache: 25. May 2022

Berlin 2022

Disaster Recovery Planning of Transportation Networks; Problem structuring and decision attributes

Acknowledgments

I would like to profoundly thank Prof. Dr. Timo Hartmann for giving me the opportunity,

resources, and liberty to conduct this research. I acknowledge his guidance and valuable

insights that helped me to better understand systematic methodological problem solving and

how to produce and communicate results with scientific and practical implications.

Moreover, he patiently and generously taught me about scientific writing and supported me

throughout this research. Timo was also the co-author of three journal publications that have

been integrated into this dissertation. The research was conducted in 2018 and 2019 at the

chair of Civil Systems- TU Berlin, while 2020 was mostly consumed for journal publications,

drafting, and submission process of the dissertation.

My sincere appreciation is dedicated to the experts from various organizations and

universities that openly shared their knowledge and participated in workshops, evaluation

sessions, interviews, or responded to surveys and questionnaires.

I would like to acknowledge the contribution of all the anonymous reviewers of the three

published papers and their feedback as related to improving chapters two, three, and four. A

few paragraphs of these papers have also been adopted in the introduction section with

modifications.

Further, I appreciate the input of Prof. Dr.-Ing. Dirk Vallée of RWTH Aachen University during

the development of the concept of my Ph.D. proposal.

I am also very grateful to Prof. Dr. Bryan T. Adey (ETH Zurich) and Prof. Dr. Pingbo Tang

(Carnegie Mellon University), who kindly agreed to join the Ph.D. examiner committee, as

well as the chairperson of the committee, Prof. Dr.-Ing. Wolfgang Huhnt (TU Berlin),

especially for his kind support during the process. Hereby, I also appreciate the suggestions

of reviewers that have been incorporated into the fifth chapter of this dissertation.

Many thanks to all my colleagues and friends from the Civil Systems Department at the

Technische Universität Berlin, at Faculty VI (Planning, Building, and Environment);

Valentina, za-Lucian, Jerson, Christoph, Farizha, Leyuan, Maryam, Nayab, and others for their

support, feedback, or proofreading.

Last but certainly not least, I am thankful to Jenny for her support, patience, and

understanding during the period of this Ph.D., as well as my sweet, lovely, little daughter Amy

Matilda for all the joy and love she gives me.

Milad Zamanifar

Erfurt- 2020

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Disaster Recovery Planning of Transportation Networks; Problem structuring and decision attributes

iii

List of Publications

This dissertation is written in an accumulative format and is founded based on the following

three published peer-reviewed journal papers. The accepted manuscript versions of those

papers have been used in this dissertation. The three papers have been slightly modified

to better integrate them into this dissertation and improve the overall consistency

and coherence.

Paper 1; Chapter 2 (Published -Open access):

Zamanifar M, Hartmann T, (2020), Optimization-based decision models for disaster recovery

and reconstruction planning of transportation networks, Journal of Natural Hazards, Vol.

104, P. 1-25, Springer. https://doi.org/10.1007/s11069-020-04192-5

Paper 2; Chapter 3 (Published-Open access):

Zamanifar M, Hartmann T, (2021), A prescriptive decision model for selecting attributes of

infrastructure risk reduction problems, Environ Syst Decis 41, 633–650 (2021).

https://doi.org/10.1007/s10669-021-09824-0

Paper 3; Chapter 4 (Preprint of the following published paper):

Zamanifar M, Hartmann T, (2021), Decision attribute for disaster recovery planning of

transportation networks; A case study, Journal of Transportation Research Part D: Transport

and Environment. Volume 93, 102771, Elsevier. https://doi.org/10.1016/j.trd.2021.102771

Summary

The way to disaster-resilient transport infrastructures is paved with effective recovery

planning. Disaster Recovery Planning of Transportation Networks (DRPTN) is a critical and

complex concept that often relies on recommendations of decision models and decision

support systems. To develop such decision systems and draft a reliable recovery plan, a well-

structured modeled problem with equitable decision attributes is essential. This dissertation

aims to address problem structuring and methodological identification of DRPTN decision

attributes. To do so, the research begins with a systematic analysis of the DRPTN

optimization models, divided into four phases: problem definition, problem formulation,

problem-solving, and model validation. For each of these phases, challenges and

opportunities are articulated, as well as suggestions to overcome the identified gaps. To

address the knowledge gaps in the problem structuring of DRPTN models, I developed a

prescriptive decision aid mechanism to assist in harnessing experts' knowledge and

recommend decision attributes for DRPTN problems. Afterward, I implemented this

framework in a real-world DRPTN problem case study to test its performance, analyze the

outcomes, and produce a systematically selected set of DRPTN decision attributes. The

findings of the research have been reported in three sections, which are outlined in detail

below.

The findings of the gap analysis suggest the presence of critical challenges within decision

attributes of existing DRPTN models, including insufficient efforts to justify and support the

adopted decision factors with theoretical arguments or formal selection processes.

Furthermore, the problem-solving phase of DRPTN modeling would benefit from adopting

meta-heuristic algorithms when explicit or implicit justifications exist, such as convexity,

linearity, or complexity analysis of the mathematical programming. In the problem

formulation phase, more effort could integrate traffic management measures and post-event

travel demand models into the formulation of network recovery. Addressing the validation

phase of DRPTN models, a benchmark system, multi-aspect simulation advances, and a

systematically developed level of confidence is needed to support the reliability of the

outcomes. The gap analysis results suggest that the method-rich but methodology-poor

phenomenon appears as a challenge for disaster recovery models.

With respect to the developed attribute-selection methodology, the framework

implementation enabled the use of experts' collaborative input in a structured manner and

promoted a disciplined decision process. The multi-stage, non-hierarchical architecture of

the framework allowed for the critical and thorough evaluation of candidate attributes in a

relatively user-friendly manner. The framework could act as a mechanism to harness

decision-makers' knowledge and help them to isolate those elements of the decision context

which are most relevant to the problem. Therefore, the recommended set is supposed to

result from a thorough, systematic process and collaborative decision-making; hence, it

offers tenable attributes for both DRPTN practice and research.

Finally, the process has led to six attributes for the case study’s road network disaster

recovery planning: 1) access level to service-providing nodes, 2) integration of link travel

Disaster Recovery Planning of Transportation Networks; Problem structuring and decision attributes

delay and traffic flow, 3) travel time improvement per recovery duration, 4) travel time

improvement per unit of resource, 5) centrality measures, and 6) link capacity. Using the

recommended set of attributes in a DRPTN model is expected to provide effective and

efficient recovery solutions that maximize mobility and accessibility in the network. Analysis

of the results suggests that the framework leads to an improved attribute set compared to

the attributes selected in an unassisted manner. The sensitivity analysis confirms that the

outranked outcomes are relatively robust against the assigned preferences. This argument

was also supported by an information entropy analysis. Both analyses suggest that

"certainty" was an incentive factor for participating experts while evaluating candidate

decision attributes.

Throughout this research, I was able to 1) identify knowledge gaps and opportunities in

optimized DRPTN decision models through conducting a systematic critical literature review

and suggest solutions for detected challenges, 2) formalize the decision process of selecting

attributes with a few innovative mathematical formulations and modeling approaches, 3)

assist and harness the knowledge of subject-matter experts with a decision aid mechanism

customized for this purpose, 4) offer the methodology as a toolkit for further application in

both science and practice, and 5) suggest a set of decision attributes of DRPTN for the case

study. Finally, besides these main contributions, I also had the chance to observe and report

on some new technical improvements, understandings, and knowledge that can be useful for

scientists and practitioners in decision analysis, traffic engineering, and disaster

management. The dissertation concludes with an emphasis on the art of problem structuring

in the DRPTN context.

Keywords: Decision attribute; Decision analysis; Disaster recovery; Transportation network;

Infrastructure; Resilience; Risk reduction.

Zusammenfassung

Der Weg zu Katastrophenresilienz Verkehrsinfrastrukturen führt über eine effektive Notfall-

bzw. Wiederherstellungsplanung (recovery planning). Die Planung der Wiederherstellung

von Verkehrsnetzen im Katastrophenfall (Disaster Recovery Planning of Transportation

Networks – DR-Planung von Transportnetzen, DRPTN) ist ein kritisches und komplexes

Konzept, das sich häufig auf Entscheidungsmodelle und Entscheidungshilfesysteme stützt.

Um solche Entscheidungssysteme zu entwickeln und einen zuverlässigen

Wiederherstellungsplan zu entwerfen, ist ein gut strukturiertes, modelliertes Problem mit

verlässlichen Entscheidungsmerkmalen erforderlich.

Ziel dieser Dissertation ist es, die Problemstrukturierung und die methodische Ermittlung

von DRPTN-Entscheidungsmerkmalen zu untersuchen. Zu diesem Zweck beginnt die

Untersuchung mit einer systematischen Analyse der DRPTN-Optimierungsmodelle, die in

vier Phasen unterteilt ist: Problemdefinition, Problemformulierung, Problemlösung und

Modellvalidierung. Für jede dieser Phasen werden Herausforderungen und Möglichkeiten

sowie Vorschläge zur Überwindung der festgestellten Defizite formuliert. Um die

Wissenslücken bei der Problemstrukturierung von DRPTN-Modellen zu schließen, wurde ein

präskriptiver Entscheidungshilfemechanismus entwickelt, mit dem das Wissen von Experten

genutzt und Entscheidungsattribute für DRPTN-Probleme empfohlen werden können. Im

Anschluss daran wurde dieses Framework in einer realen DRPTN-Fallstudie implementiert,

um seine Leistungsfähigkeit zu testen, die Ergebnisse zu analysieren und eine systematisch

ausgewählte Menge von Entscheidungsattributen für das DRPTN zu erstellen. Die

Forschungsergebnisse wurden in drei Abschnitten zusammengefasst, die im Folgenden kurz

beschrieben werden.

Die Ergebnisse der Analyse der Wissensdefizite deuten darauf hin, dass bei den

Entscheidungsattributen bestehender DRPTN-Modelle Probleme bestehen. Dazu gehören

unzureichende Bemühungen, die angenommenen Entscheidungsfaktoren mit theoretischen

Argumenten oder formalen Auswahlprozessen zu begründen und zu stützen. Darüber hinaus

würde die Problemlösungsphase der DRPTN-Modellierung von der Anwendung

metaheuristischer Algorithmen profitieren, wenn es explizite oder implizite Begründungen

wie Konvexität, Linearität oder Komplexitätsanalyse der mathematischen Programmierung

gibt. In der Phase der Problemformulierung könnten mehr Anstrengungen unternommen

werden, um Verkehrsmanagementmaßnahmen und Modelle für die Verkehrsnachfrage nach

dem Notfall (bzw. der Naturkatastrophe) in die Formulierung der

Netzwerkwiederherstellung zu integrieren. Für die Validierungsphase von DRPTN-Modellen

sind ein Benchmark-System, Fortschritte bei der multiperspektivischen Simulation und ein

systematisch entwickeltes Vertrauensniveau erforderlich, um die Zuverlässigkeit der

Ergebnisse zu erhöhen. Die Ergebnisse der Analyse der Wissenslücken deuten darauf hin,

dass das methodenreiche, aber methodologisch schwache Phänomen eine Herausforderung

für Disaster-Recovery-Modelle darstellt.

In Bezug auf die entwickelte Methodik zur Auswahl von Attributen ermöglichte die

Implementierung des Frameworks die Nutzung des gemeinschaftlichen Inputs von Experten

in einer strukturierten Weise und förderte einen disziplinierten Entscheidungsprozess. Die

Disaster Recovery Planning of Transportation Networks; Problem structuring and decision attributes

vii

mehrstufige, nicht-hierarchische Architektur des Frameworks ermöglichte die kritische und

gründliche Bewertung von möglichen Attributen auf relativ benutzerfreundliche Weise. Das

Framework könnte als Mechanismus dienen, um das Wissen der Entscheidungsträger

nutzbar zu machen und ihnen zu helfen, diejenigen Elemente des Entscheidungskontexts

einzugrenzen, die für das Problem am wichtigsten sind. Aus diesem Grund sollte die

empfohlene Menge das Ergebnis eines gründlichen, systematischen Prozesses und einer

kollaborativen Entscheidungsfindung sein; dadurch bietet es sowohl für die DRPTN-Praxis

als auch für die Forschung brauchbare Kriterien.

Die Entscheidungsträger haben sechs Attributen ausgewählt, die in die Notfallplanung für

das Teheraner Straßennetz einfließen sollen: (1) Art des Zugangs zu Serviceknotenpunkten;

(2) Integration von Reisezeitverzögerung und Verkehrsfluss auf den Straßen; (3)

Verbesserung der Reisezeit pro Wiederherstellungsdauer; (4) Verbesserung der Reisezeit

pro Ressourceneinheit; (5) Zentralitätsmaße und (6) Kapazität der Verbindungen. Es wird

erwartet, dass die Verwendung der empfohlenen Attribute in einem DRPTN-Modell effektive

und effiziente Wiederherstellungslösungen bietet, die die Mobilität und Zugänglichkeit im

Verkehrsnetz maximieren. Die Analyse der Ergebnisse deutet darauf hin, dass das

Framework zu einem verbesserten Attributset im Vergleich zu denjenigen Attributen führt,

die ohne Unterstützung ausgewählt wurden. Die Sensitivitätsanalyse bestätigt, dass die

übergeordneten Ergebnisse relativ robust gegenüber den zugewiesenen Präferenzen sind.

Dieses Argument wurde auch durch eine Analyse der Informationsentropie gestützt. Beide

Analysen deuten darauf hin, dass „Gewissheit“ ein Anreizfaktor für die teilnehmenden

Experten bei der Bewertung von Entscheidungsattributen war.

Im Rahmen dieser Forschungsarbeit konnte ich (1) Wissenslücken und Möglichkeiten in

optimierten DRPTN-Entscheidungsmodellen durch eine systematische kritische

Literaturanalyse identifizieren und Lösungen für die erkannten Herausforderungen

vorschlagen; (2) den Entscheidungsprozess zur Auswahl von Attributen mit einigen

innovativen mathematischen Formeln und Modellierungsansätzen formalisieren; (3) das

Wissen von Fachexperten mit einem für diesen Zweck angepassten

Entscheidungshilfemechanismus nutzbar machen; (4) die Methodik als Toolkit für die

weitere Anwendung sowohl in der Wissenschaft als auch in der Praxis anbieten; und (5) eine

Menge von Entscheidungsmerkmalen von DRPTN für die Fallstudie vorschlagen. Daneben

ergab sich auch die Möglichkeit, einige neue technische Verbesserungen, Erkenntnisse und

Wissen zu beobachten und darüber zu berichten, die für Wissenschaftler und Praktiker in

den Bereichen Entscheidungsanalyse, Verkehrstechnik und Katastrophenmanagement von

Nutzen sein können. Die Dissertation schließt mit einem Hinweis auf die Bedeutung und

Kunst der Problemstrukturierung im DRPTN-Kontext.

Schlüsselwörter: Katastrophenresilienz, Wiederherstellung Entscheidungsverfahren,

Verkehrsinfrastrukturen, Entscheidungshilfemechanismus, katastrophenschutz,

katastrophenrisikomanagement

 
viii 
Table of Contents 
 
 
Acknowledgments .............................................................................................................. i 
List of Publications .......................................................................................................... iii 
Summary .......................................................................................................................... iv 
 Zusammenfassung .......................................................................................................... vi 
Table of Contents ........................................................................................................... viii 
Introduction .............................................................................................................. 2 
1 DRPTN: Disaster Recovery Planning of Transportation Networks ........................ 2 
2 Problem Structuring ..................................................................................................... 6 
3 Problem Structuring in DRPTN Context ................................................................... 7 
4 A Short Story: An Overview of the Study and Area of Focus .................................. 9 
5 Study Domain .............................................................................................................. 11 
5.1 The Context of the Case Area .................................................................................. 12 
5.2 Disaster Scenario ...................................................................................................... 14 
6 Research Objective and Contributions ..................................................................... 15 
7 Research Gap and Motivations ................................................................................. 17 
7.1 Motivation and Knowledge Gap in the Development of Objective 1 ...................... 19 
7.2 Motivation and Knowledge Gap in the Development of Objective 2 ...................... 20 
7.3 Motivation and Knowledge Gap in the Development of Objective 3 ...................... 22 
8 Research Questions ..................................................................................................... 23 
9 Research Methods ....................................................................................................... 24 
10 Outline of the Dissertation ......................................................................................... 25 
11 References .................................................................................................................... 27 
Decision Models for DRPTN; Review and Analysis............................................ 32 
1 Summary ..................................................................................................................... 32 
2 Introduction ................................................................................................................ 33 
3 Optimization-based Decision-Making Models and DRPTN ................................... 37 
3.1 Problem Definition ................................................................................................... 39 
3.2 Problem Formulation................................................................................................ 40 

 Disaster Recovery Planning of Transportation Networks; Problem structuring and decision attributes  
 
ix 
3.3 Problem Solving ....................................................................................................... 41 
3.4 Model Verification and Validation .......................................................................... 43 
4 Review and Analysis Methodology ........................................................................... 44 
4.1 Search Strategy......................................................................................................... 44 
4.2 Content Analysis ...................................................................................................... 45 
5 Findings ....................................................................................................................... 47 
5.1 Problem Definition ................................................................................................... 47 
5.2 Problem Formulation ............................................................................................... 49 
5.3 Problem Solving ....................................................................................................... 51 
5.4 Model Validation ..................................................................................................... 53 
6 Discussion and Suggestions ........................................................................................ 54 
6.1 Problem Definition ................................................................................................... 54 
6.2 Problem Formulation ............................................................................................... 56 
6.3 Problem Solving ....................................................................................................... 58 
6.4 Model Validation ..................................................................................................... 60 
7 Summary and Conclusion .......................................................................................... 62 
8 References ................................................................................................................... 64 
A Methodology for Selection of Attributes........................................................... 72 
1 Summary ..................................................................................................................... 72 
2 Introduction ................................................................................................................ 73 
3 Knowledge Gap and the Necessity ............................................................................ 75 
4 Current Approaches towards the Selection of Attributes ...................................... 78 
5 Evaluation Factors and the Decision Environment ................................................. 81 
6 Methodology and the Developed Framework .......................................................... 84 
6.1 Preference Elicitation ............................................................................................... 85 
6.2 Models of Transition and Aggregation .................................................................... 88 
6.3 The proposed Framework ........................................................................................ 91 
6.4 Methods of Implementation ..................................................................................... 94 
7 Result and Synthase ................................................................................................... 98 
7.1 Performance of the Framework in the Implementation Process .............................. 98 
7.2 Synthesis of the Framework’s Outcome and Feedback of Participating DMs ...... 101 
8 Discussion .................................................................................................................. 104 
9 Limitations ................................................................................................................ 107 
10 Conclusion ................................................................................................................. 108 
11 References ................................................................................................................. 110 

 
x 
Decision Attributes of DRPTN ............................................................................ 118 
1 Summary ................................................................................................................... 118 
2 Introduction .............................................................................................................. 119 
3 Disaster, Transportation Network, and Recovery Process ................................... 121 
4 Knowledge Gap and Motivation ............................................................................. 123 
5 Methods and the Research Design .......................................................................... 124 
5.1 Problem Structuring ............................................................................................... 125 
5.2 Relative Importance of Compensatory Factors ...................................................... 127 
5.3 Evaluation and Value Aggregation ........................................................................ 128 
6 Main results ............................................................................................................... 129 
6.1 Evaluation and Value Tree ..................................................................................... 129 
6.2 Recommended Set .................................................................................................. 131 
6.3 The Selected Set and DRPTN Literature ............................................................... 133 
7 Sensitivity Analysis ................................................................................................... 134 
8 Discussion .................................................................................................................. 137 
8.1 Analysis of the Attribute Set .................................................................................. 137 
8.2 Practical Implications ............................................................................................. 139 
9 Limitations and Future Research ........................................................................... 140 
10 Conclusion ................................................................................................................. 141 
11 References .................................................................................................................. 143 
Conclusion ............................................................................................................. 150 
1 Summary and Main Findings .................................................................................. 150 
2 Contributions ............................................................................................................ 155 
2.1 Contributions toward Meeting Objective 1 ............................................................ 156 
2.2 Contributions toward Meeting Objective 2 ............................................................ 157 
2.3 Contributions toward Meeting Objective 3 ............................................................ 158 
2.4 Application of Findings .......................................................................................... 159 
3 Future Research, Open Questions, and Remaining Gaps .................................... 160 
3.1 Sensitivity to Local Minima and Converting Objectives to Constraints ................ 160 
3.2 Future research on the Implementation of the Framework .................................... 161 
3.3 Does Preference for a Certain Objective Impact the Selection of Attributes? ....... 162 
3.4 Integrating Traffic Management of Networks with Recovery Planning ................ 163 
3.5 DRPTN modeling: Do Social Vulnerability Variables Matter? ............................. 163 
3.6 Lack of Validation Tools........................................................................................ 164 
4 Key Recommendations for Decision-Makers and Research................................. 165 

Disaster Recovery Planning of Transportation Networks; Problem structuring and decision attributes

5.4.1 Problem Structuring Necessity in the DRPTN Modeling Context ........................ 166

5.4.2 Modeling a DRPTN Problem ................................................................................. 168

5.4.3 Attributes for a DRPTN Model .............................................................................. 171

5.5 The Art of Modeling in Disaster resilience planning Contexts ............................ 175

5.6 References ................................................................................................................. 178

Appendix A .................................................................................................................... 180

Appendix B .................................................................................................................... 182

xii

LIST OF ABBREVIATIONS AND ACRONYMS

AADT Annual Average Daily Traffic

ADT Average Daily Traffic

AWT Average Weekday Traffic

DA Decision Analysis

DM Decision-Maker

DRPTN Disaster Recovery Planning of Transportation Network

DRR Disaster Risk Reduction

DRM Disaster Risk Management

DSS Decision Support System

EIII Error of the third kind

GA Genetic Algorithm

GIS Geographic Information System

IESDS Iterated Elimination of Strictly Dominated Strategies

MADM Multiple Attribute Decision Making

MAVT Multiple Attribute Value Theory

MCDA Multiple Criteria Decision Analysis

MCDM Multiple Criteria Decision Making

MODM Multiple Objective Decision Making

NP Non-deterministic Polynomial-time

O-D Origin-Destination

S-P Service-Providing

SAW Simple Additive Weighting

TOPSIS Technique of Order Preference Similarity to the Ideal Solution

VIKOR VIseKriterijumska Optimizacija I Kompromisno Resenje (Serbian)

Disaster Recovery Planning of Transportation Networks; Problem structuring and decision attributes

Chapter I

INTRODUCTION

“What is missing in most decision making methodologies is a philosophical approach and

methodological help to understand and articulate values and to use them to identify decision

opportunities and to create alternatives.”

Ralf A. Keeney (1992)

I-Introduction

1 Introduction

1.1 DRPTN: Disaster Recovery Planning of Transportation

Networks

Disaster Recovery Planning of Transportation Networks (DRPTN) is a critical and

complex concept that often relies on recommendations of decision models and

decision support systems. To develop such decision systems and draft a reliable

recovery plan, a well-structured modeled problem with equitable decision attributes

is essential. This dissertation aims to address the problem structuring and

methodological identification of DRPTN decision attributes in order to provide a

foundation for risk-informed decision-making for road network recovery in the

aftermath of disasters.

Natural, anthropogenic, or socio-natural hazards (and their combination) can create

disasters in vulnerable, exposed, and non-resilient societies. On the one hand, we

might not be able to contain or restrain rapid-onset natural hazards in the near

future. Nor is it likely that we cease triggering nature to avoid the escalation of the

intensity and extensity of socio-natural and climate change-induced hazards. On the

other hand, mitigating the exposure of critical infrastructures, as broad interwoven

networks on which our civilizations are built, comes at an extreme cost, which

renders risk transfer an unreasonable solution. Consequently, in the context of

infrastructure Disaster Risk Management (DRM), alternatives are limited to two main

concepts of “reducing vulnerability” and “increasing resilience” of infrastructures.

Next to the measures that mitigate the risk of disaster occurrence, resilience in the

transportation network can be defined through adaptive, absorptive, and restorative

capacities. A massive share of these resilience properties is borne by recovery

planning to restore the transportation network’s performance to a state that serves

Disaster Recovery Planning of Transportation Networks; Problem structuring and decision attributes

the affected community in the times that it is most needed (Bruneau et al. 2003;

Zhang et al. 2017; Kurth et al. 2020). In urban areas, the transportation network is

one of the most exposed physical infrastructures. Nevertheless, proactive planning

for post-event efforts markedly increases the resilience and capacity of the

transportation network to recover from the adverse impacts of extreme natural

phenomena (Naga and Fan 2017; Quarantelli 1999; Rouhanizadeh 2019).

Transportation systems present both prosperity and calamity. They not only provide

mobility and accessibility for people and supply chains but also for armies and

diseases. A transportation system is a cyber-physical critical infrastructure system

that, as a “lifeline,” provides critical utilities and services vital for the well-being and

operation of the community it serves. The socioeconomic functioning of many

individuals, enterprises, and critical services depends on the efficient, fast,

sustainable, disciplined, optimized, and safe operation of transportation networks.

Almost all components of social and economic systems directly or indirectly interact

with the transportation system (Cova and Cogner 2004). However, a radical,

disruptive impact on the performance of a transportation network can be easily

perceived as a disaster that imposes a direct threat to individuals and disrupts the

socioeconomic continuity. Table 1.1 shows the direct expected annual damage cost

due to the destruction of road and rail assets by hazards, excluding landslides (Koks

et al. 2019).

Table 1.1: Total expected annual direct damage per hazard in the road and rail sector.

Multi-hazard refers to the aggregate of floods, cyclone, and earthquake.

Hazard

Median of Annual expected

Damage (approximately)

Flood (River, surface, coastal)

88.9 %

9.6 Billion USD

Earthquake

7.3 %

1 Billion USD

Cyclone

3.8 %

0.4 Billion USD

Multi-hazard

100

11 Billion USD

Hazards cause damage to a transportation network's physical components, disrupt

I-Introduction

its cyber-physical administration, and drastically shift the behavior of its users. It also

impedes users' access to essential services and products as well as the access for

users who are critical to the performance of urban systems. Convergence of

susceptibility with exposure and non-resilience is a catalyst for the transformation of

a hazard to a disaster in transportation networks. As Figure 1.1 shows, transportation

networks, globally, are exposed and susceptible to hazards, which render the post-

hazard failure of this system a likely event.

Figure 1.1: Global multi-hazard transport infrastructure exposure (Source: Koks et al.

2019

)

A damaged road network is both a key challenge and solution for search-and-rescue

operations in the emergency response phase, as well as for the community recovery

and restoration of socioeconomic affairs in the recovery phase. When a

transportation network is not capable of offering the service it was expected to,

disaster emerges. Disaster in a transportation network is a set of disruptive

conditions that hinder connectivity, accessibility, and mobility, leading to an extreme

loss of network functionality. A road network is the sole post-disaster lifeline that

grants mass mobility and provides access to essential origin and destinations (ODs)

within the affected area. This lifeline is not only structurally vulnerable to hazards

but also causes social non-structural vulnerabilities and losses to affected

communities. Recovery planning strongly contributes to the resilience of the

transportation system as it can alleviate the calamitous effect of hazards and reduce

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Disaster Recovery Planning of Transportation Networks; Problem structuring and decision attributes

network downtime, while enhancing the network’s performance and restoring social

life. In fact, resilience, in a transportation context, is partially defined by expedient,

effective, and efficient recovery. An ideal recovery and reconstruction planning

eventually addresses various post-event issues such as emergency, technical, and

socio-economical aspects, since disaster recovery is more of a social process than a

mere technical one (Nigg 1995; Lubashevskiy et al. 2017). Providing low-cost, high-

impact solutions; accelerating recovery ratio; and promptly establishing access to

critical assets are all crucial features of recovery operations that highlight the vital

role of Disaster Recovery Planning of Transportation Network (DRPTN). Therefore,

successful planning for the disaster recovery process could play an important role in

increasing the resilience of an urban area after hazard-induced disasters, thus

demonstrating the importance of research in this field. DRPTN is the series of

prescribed decision recommendations that respond to the prioritization challenges

of recovery operations. DRPTN provides sets of analytic interventions for which

elements of a transportation system should be repaired first or which sequence of

post-disaster repair and rehabilitation measures yields better system performance

by proving more efficient, covering a wider amount of users, better responding to the

needs of those who suffer most, having a shorter recovery interval, or a higher rate

of recovery. It can be formulated as a ranking model and can either provide a

compromise solution to the problem of prioritization of multiple criteria or an

optimized solution with one or more objectives. On this ground, DRPTN covers

prescriptive decision models, constructed to respond to an extreme hazard that 1)

exhibits structural damage to the transportation network’s components, 2) directly

causes major operational disruption to the traffic functionality of the network or part

of it, and 3) can be alleviated only by intervention through physical construction, such

as repair and reconstruction operations.

In the aftermath of a disaster in a transportation system, decision-makers (DMs),

either authorities, owners, or operators of infrastructures, seek optimized decision

recommendations for the recovery process. To support this process, studies develop

DRPTN decision models that prioritize reconstruction operations on the network’s

components. DRPTN decision models, as any decision model, are based on the

I-Introduction

objectives that reflect the interests, concerns, and values of stakeholders and all

affected parties concerning the decision context. A decision context is a setting in

which the decision problem is recognized. Attributes measure the level to which an

objective is achieved in a given decision alternative and/or represents the essential

characteristic of the modeled system that directly impacts objective values. Achieving

a representative, effective, and reliable decision-making model for disaster recovery

planning requires a well-thought-out set of decision attributes, among other

properties. Equitable attributes of a decision model indicate that the problem is well

perceived and properly structured. Determining the essential characteristics of the

modeled problem and its attributes falls into the category of problem structuring as

an indispensable and challenging task of DRPTN decision modeling, which is

introduced in the next section.

1.2 Problem Structuring

Developing a decision model becomes difficult when the problem is not well

perceived, defined, or characterized. The first logical step of modeling a shared reality

or rationality of a prescriptive decision process is to apprehend the current and

desired state that the model is designed to represent and to frame the problem

accordingly. Toward this understanding, in-depth typological investigations of the

problem and its model are essential to avoid transferring the complexity of the

problem into the problem-solving process. This investigation can be achieved

through a formal problem structuring approach. Problem structuring is the process

of understanding, identifying, and characterizing a problem that ultimately reduces

the likelihood of committing the error of the third kind (Type III error or EIII),

wherein the incorrect problem is solved correctly, while the correct problem remains

concealed or only partially solved (Kimbaal 1957). It is acknowledged that the

attempt of solving a problem is secondary to understanding it, and the influence of

contextual factors on understanding the decision process is significant (Dillon 1998;

Baron 2007; Franco and Montibeller 2009; Belton and Stewart 2010). Mitroff and

Featheringham (1974) emphasize that “one of the most important determinations of

a problem’s solution is how that problem has been represented or formulated in the

Disaster Recovery Planning of Transportation Networks; Problem structuring and decision attributes

first place” (Mitroff and Featheringham 1974). Problem structuring stresses first

understanding the problem before attempting to solve it. von Winterfeldt (1986)

defines problem structuring as “a process of translating an initially ill-defined

problem into a set of elements, relations, and operations” and later points out that

identifying a problem’s elements is the primary task of problem structuring. Corner

et al. (2001) refer to problem structuring as the design stage, where objectives,

decision attributes, and alternatives are identified. Further, Belton and Stewart

(2010) highlight that although problem structuring does not conclude the decision

process, sometimes a well-structured problem renders the solution “self-evident.”

A major task of problem structuring is selecting decision attributes. Attributes clarify

the meaning of each objective and measure the consequences of different alternatives

(Keeney and Gregory 2005). The attribute set of a decision model represents

essential problem-related characteristics and the performance of the modeled

system. The degree to which this representativeness is preserved within an attribute

indicates its directness. The primary purpose for establishing an effective set of

attributes is to disaggregate a complex decision environment into more analytically

tractable components while maintaining the representativeness and collectivity of

the modeled problem as “direct” as possible. Therefore, an effective attribute set of a

problem is likely to yield a decision model that is representative, direct, and

complete, thus providing some degree of confidence in the reliability of the output.

Identifying the underlying decision variables and decision factors is considered a

preliminary step and a major cornerstone of the problem-structuring process

(Corner et al. 2001; Keeney 1992).

1.3 Problem Structuring in DRPTN Context

Belton and Stewart (2010) argue that some problems in decision analysis can be

termed “messy” because both the definition and solution to the problem are

debatable. The messy nature of decision analysis escalates when it sits in the context

of a problem that involves stochastic and uncertain variables in a low-validity

decision environment such as disaster recovery planning. A key component to

address messy-type problems is the use of facilitation to identify values and frame

I-Introduction

the multi-criteria problem (Keeney and Mcdaniels 1992). The selection of a tenable

attribute set is one important task within this facilitation process. This dissertation

offer this facilitation by exploring the problem typology of DRPTN, designing a

methodology to assist the selection of DRPTN attributes, and implementing this

methodology in a real-world instance of a DRPTN problem.

The significant necessity of problem structuring for DRPTN lies in the fact that

DRPTN decision modeling, as is the case for many complex decision analyses, is an

error-prone task that mainly relies on the modelers’ judgment (Phillips-Wren et al.

2019; Winter et al. 2018; Beven et al. 2015). This inevitable subjectivity may result

in committing the error of the third kind (Mitroff and Featheringham 1974). The

increase in the likelihood of errors that results from failing to properly structure a

DRPTN problem is costly for both the public and authorities due to the impacts of

decisions in this sensitive context, since the critical nature of the disaster recovery

problem exponentially intensifies the consequence of inaccuracies in DRPTN models.

This criticality and sensitivity are due to the cascading impact of disasters in urban

areas that propagate on a wide scale and wreak havoc beyond damage to physical

assets, as they also adversely affect people, economies, environments, and social

systems (Kadri et al. 2014). Furthermore, the non-observability of disaster recovery

activities makes the situation all the more difficult, as there is sparse applicable data

on disasters that can be compared with the output of developed DRPTN models for

evaluation purposes (Sargent 1996; Day et al. 2009; Kadri et al. 2014). Even if data is

partly available, performing a retrospective test to validate a model is cumbersome,

if not impossible, due to the uncertainties and degree of inconsistency between two

datasets representing previous and probable future disasters (Leskens et al. 2014;

Celik and Corbacioglu 2010). Non-observable models represent complex problems

where real-time data on the system's current and past performance cannot

characterize its future behavior, as the modeled system has very little similarity with

the past or current state of the system. In a non-observable problem, the regularity

of the current state of the system (performance and property) is not valid for the

problem under consideration, which yields a low-validity decision environment. The

non-observability of a problem emphasizes the pressing need for efforts on problem

Disaster Recovery Planning of Transportation Networks; Problem structuring and decision attributes

structuring of prescriptive models that represent critical and sensitive real-life

problems. Therefore, the selection of viable decision attributes as well as a

methodological problem structuring is of the utmost importance for disaster

recovery planning problems.

1.4 A Short Story: An Overview of the Study and Area of Focus

This study is built upon an old premise that “a problem well put is half solved”

(Dewey 1938). This assumption was the motivation of this research, that the attempt

to delineate a solid, well-grounded problem structuring in DRPTN context is, first,

“imperative,” and second, “not yet sufficiently addressed” in the literature. I

investigated the latter by conducting a systematic review within the identified

DRPTN literature and realized that problem structuring is vastly overlooked. Studies

take a well-framed problem as a starting point; thus, very few attempts have been

made to generate decision attributes that can be supported by a formal approach or

logical arguments. For the second assumption, I harnessed the fact that problem

structuring is crucial for decision analysis modeling in general, based on existing,

well-established literature of decision analysis, which allowed me to generalize this

fact to the sensitive, critical, and complex context of DRPTN. Once my field of inquiry

became clear, I designed a strategy to approach it. Attacking the identified problem, I

borrowed from the prescriptive decision theory concept to build a model that

assisted experts with turning their input into decision attributes of a DRPTN problem.

After that, I implemented this methodology and sets of methods in a real-world case

study to observe the model's performance and report the outcomes, which are

decision attributes of DRPTN for the Iranian context. On this ground, I collected

attributes that 46 DRPTN papers suggested and extracted attributes based on the

opinions of 23 experts in disaster management. Then I conducted a workshop asking

four experienced decision-makers and city planners (who each possessed authority,

knowledge, experience, and stake) to evaluate those attributes using the developed

framework. I was hoping that the framework could assist (or even guide) their

intuitive opinion to a more rational, context-dependent knowledge and allow them

to critically – yet at the same time simply – assess both attributes and the

I-Introduction

combination of them, which constitute a set. For this evaluation process, I used ten

criteria as evaluation factors within three sequential stages. Each stage had its own

evaluation factors and, therefore, its own rule of evaluation as the decision rule. The

first stage operated under a non-compensatory decision rule with three evaluation

factors. The second stage functioned in a compensatory fashion with four evaluation

factors. The first two stages evaluate individual attributes as a member of an ideal

set. Finally, in the last stage, DMs could evaluate sets of attributes with three factors

under the optimal decision rule. I built the aggregation method by integrating

Elimination by Aspect and Multi-Attribute Value Theory to aggregate experts' inputs,

which are both well-known developed Multi-Attribute Decision-Making techniques.

I also developed a cardinal rank-based weighting model to find trade-offs among

some evaluation factors that operate under the compensatory decision rule by using

the input of decision analysis experts. As a result of this implementation of the

framework in the Iranian DRPTN context, I showed that the developed methodology

could systematically harness the knowledge of decision-makers and perform well for

the objective for which it was designed. The framework was relatively user friendly,

traceable, and inclusive. It delivered a set of six attributes for the context of the case

study. I also performed several analyses on the results and performance of attributes,

as well as a post-workshop survey and an interview to assess the performance of the

framework and the quality of the attributes produced.

Throughout this research, I was able to 1) identify knowledge gaps and opportunities

in optimized DRPTN decision models through conducting a systematic critical

literature review and suggest solutions for detected challenges; 2) formalize the

decision process of selecting attributes with a few innovative mathematical

formulations and modeling approaches; 3) assist and harness the knowledge of

subject-matter experts with a decision-aid mechanism customized for this purpose;

4) present the methodology as a toolkit for further application in both science and

practice; and 5) suggest a set of decision attributes of DRPTN for the case study.

Finally, besides these main contributions, I also had the chance to observe and report

on some new technical improvements, understandings, and knowledge that can be

useful for scientists and practitioners in decision analysis, uncertainty analysis, traffic

Disaster Recovery Planning of Transportation Networks; Problem structuring and decision attributes

engineering, and disaster management.

Problem structuring for Disaster Recovery Planning of Transportation Networks

(DRPTN) encompasses the fields of civil engineering, operations research, and

disaster management. Within the field of disaster management, this conducted study

is based on notions and concepts of urban emergency management and resilient

infrastructure, focusing on urban recovery planning. It also draws on civil

engineering to incorporate knowledge of traffic and transportation planning with a

touch of construction management. Insights offered by Operations Research also

enrich this study while applying decision analysis and developing decision models.

Figure 1.2 shows the overlap of the three major disciplines and the research area of

focus. In bringing these fields together, this dissertation links the domain of disaster

recovery planning to decision modeling in the context of transportation networks to

provide a foundation for decision analysis in (re)construction management and

recovery planning of transportation networks.

Figure 1.2: The discipline-wise focus area of this research

1.5 Study Domain

The problem of selecting DRPTN attributes exists in general but is contextually

specific for each transportation network setting. Accordingly, the DRPTN problem

I-Introduction

requires contextualized inputs based on local urban properties such as social

parameters, topologies, vulnerability states, and resilience capacities. The knowledge

of those properties can be obtained from local disaster recovery decision-makers,

owners, and operators of urban infrastructures. Therefore, I implemented the

proposed framework in the context of Tehran’s DRPTN, to realize the opportunity of

harnessing the experience and knowledge of decision-makers who have been

engaged with urban disaster management and transportation planning with first-

hand experience and current involvement in the field.

1.5.1 The Context of the Case Area

Iran is a hazard-prone and disaster-prone country. Hazards such as deforestation,

drought, earthquakes, floods, landslides, and wildfires impose tremendous long-term

economic, social, and environmental losses. Among common hazards, earthquakes

are a major perceived hazard risk in the country. The Greater Iranian plateau embeds

active faults and volcanic high-surface elevations along the Himalayan-Alpied

earthquake belt. Tehran, the capital of Iran, is exposed to droughts, floods, extreme

heat, freeze-thaw, and earthquakes. The seismic status of the Tehran region

subordinates to the geomorphologic and tectonic condition of the Iranian plate. This

area is located over alluvium sediments of the southern foothills of the central Alborz

Mountains accommodating Gondwana–Eurasia collision in the Late Triassic along the

Alpine–Himalayan orogeny belt. Due to the northward convergence of the great

Iranian plateau and Eurasia, the southern foothill areas of the Alborz Mountains are

relatively active zones, subject to massive tectonic stresses (Kamranzad et al., 2020).

According to historical notes, major earthquakes have destroyed Tehran at least six

times in history (Ghodrati Amiri et al. 2003). Based on the pattern of major

earthquakes in Tehran’s history, an earthquake of magnitude 7 is rather likely every

158 years as the estimated recurrence interval (Ambraseys and Melville 1982;

Ghodrati Amiri et al. 2003). The last major earthquake struck Tehran 191 years ago.

Besides the consistent seismic risk in the Tehran metropolitan area, the city currently

and frequently suffers hazards such as floods, landslides, cave-ins, subsidence, fire,

snow, frost, and extreme heat. Tehran’s transportation network consists of over 200

bridges, 931 km of highways and freeways, 1,053 km of main streets, 1,552 km of

Disaster Recovery Planning of Transportation Networks; Problem structuring and decision attributes

collector and access streets, 18.7 km of bus rapid transit track, and 460 km of subway

track that operates 18.9 million daily trips (TDTM 2017). Figure 1.3 shows some

components of Tehran’s transportation network.

Figure 1.3: Tehran network modeled in QGIS with transportation network components

As a metropolitan area with a population of over 9.000.000

and a total area of

around 660 square kilometers, Tehran is developed over an asymmetric complex

lifeline network and intricately interwoven infrastructures. The city consists of

structurally and socially decayed urban environments and vulnerable physical

structures. On the one hand, fragile resilience capacities, ripple-effect-prone civil

systems, and fragmented coordination in crisis management associated with slow,

unorganized decision-making flows raise the likelihood of transforming hazards into

disasters. On the other hand, Given the experience of confronting multiple natural

and human-made hazards, there is empirical knowledge and practical experience

among the local disaster managers and city planners, making it a tenable case for

Estimated population according to Tehran municipality website (accessed in 2020).

I-Introduction

study. Additionally, due to the author's background, the possibility of identifying,

coordinating, and inviting the experienced, educated, and active decision-makers and

subject-matter experts who would be willing to participate in the study was the

operational motivation of the case selection.

1.5.2 Disaster Scenario

There are usually three main temporal phases after a disaster: emergency response,

medium-term recovery, and long-term reconstruction (Feng and Wang 2003; Joakim

2011; Quarantelli 1999). Although the borders between these phases are amorphous

and overlap, restoration planning in each of the three phases seeks different targets

and addresses different needs. Thus, each phase requires its own specific planning

approach. The first phase is called the emergency response or immediate relief; it

immediately follows the event (after the confusion period) and usually lasts between

three to seven days after the disaster. Common activities include search-and-rescue

operations, delivering medical care, debris removal, mass care, and providing shelter.

The recovery phase begins during or after the emergency response. This second

phase comprises all actions that restore the community function and civil

performance to return the situation to a safe and acceptable level, which might not

necessarily be the same as the pre-event condition. Mobility and accessibility

recovery, medical care, lifeline rehabilitation, and sociocultural and economic

continuity have higher significance in this period, which can last for months. The

distinction between the recovery and response phases is important because the

skills, resources, objectives, time horizons, and stakeholders of the response and

recovery phases are dramatically different. The last phase is the long-term

reconstruction, which contains all measures for increasing the mitigation of and

preparedness for disasters, implementing sustainable development, and completing

large-scale reconstruction projects that may take more than two years.

In this dissertation, the focus is on mid-term recovery operations. The disaster

scenario includes a major, sudden-onset hazard that creates small-scale and large-

scale disasters, which have a disruptive impact that lasts more than weeks. Based on

these parameters, a disaster scenario was presented to the participating DMs to

familiarize them with the targeted problem. In addition, data of the Tehran region,

Disaster Recovery Planning of Transportation Networks; Problem structuring and decision attributes

which is currently the information available for decision-making in disaster

situations, was presented to DMs. It includes demographic data of the population

such as age, gender, employment situation, education condition, and income rate as

well as traffic properties of links and the network including peak hour daily traffic

volume and Annual Average Daily Traffic (AADT) of the links, 2D-visualized geometry

of the network, along with the location and type of critical facilities and

infrastructures of the region. Geospatially assigned information was also mapped and

visualized to specify the problem's properties and the situation for which the decision

attributes are needed. Appendix (A) provides examples of information that was

presented to familiarize DMs with the disaster scenario. Once the experts were

familiarized with the problem environment and a shared understanding of a scale

and type of disaster was achieved, knowledge extraction began. Chapters three and

four demonstrate this process in detail.

1.6 Research Objective and Contributions

This research contributes to the modeling process of constructing disaster recovery

DSSs and paves the way for a tenable problem-structuring phase of decision analysis

in the DRPTN context. The need for decision-aiding mechanisms to support building

DRPTN models motivates this research, since the quality of DRPTN models has a

substantial impact on socio-economic losses in disaster-exposed communities and,

more importantly, impacts the health and well-being of the affected population.

Therefore, this research targets capacity building to increase the resilience of urban

areas by offering methods and materials to improve the post-disaster recovery

planning process of lifelines. More specifically, the objectives of the study are:

1) Identifying knowledge gaps and emerging methodological demands for

optimization-based DRPTN models to understand what improvements are necessary

in DRPTN models:

1-1) Providing in-depth analytical understanding on the application of

optimization programing in DRPTN models and micro-analysis of the

methodology of current studies;

1-2) Providing suggestions to improve the reliability of DRPTN models and

I-Introduction

their application in real-life instances of disaster problems;

1-3) Discussing newly detected gaps and improvement areas for optimization

programing in the DRPTN context;

1-4) Exploring the possibility of opening new discussions and suggestions to

overcome the detected gaps and future directions of DRPTN research.

2) Supporting analysts who design DRPTN models or develop DSSs for disaster

recovery applications with a framework that serves as a decision-aiding toolkit and

allows for selecting tenable decision attributes:

2-1) Assisting decision-makers to make informed choices on decision attributes

in a structured manner and facilitate elicitation of their knowledge toward

selecting a reliable attribute set;

2-2) Formulating the attribute-selection process as a prescriptive choice model;

2-3) Channeling the opinion/preference of experts with a decision-aiding

mechanism to produce the knowledge of DRPTN values.

3) Suggesting a viable set of key attributes for disaster recovery planning within the

Tehran transportation network as an example:

3-1) Collecting data from DRPTN literature and experts in disaster

management with regard to attributes of a DRPTN;

3-2) Harnessing the knowledge of DMs as subject-matter experts for

identifying DRPTN key attributes with the implementation of the

developed framework;

3-3) Obtaining a degree of confidence in the performance of the developed

framework and quality of its outcome.

The following explanation reflects the interrelation and coherency of the three

objectives: Meeting the first objective (knowledge gaps) drives the second objective

(the framework), while the second objective provides the means for obtaining the

third one (selected attributes). Therefore, the outcome of the first objective is

identifying the demand for a systematically produced and equitable attributes set of

DRPTN problems as an emerging need of the DRPTN field. To meet the second

Disaster Recovery Planning of Transportation Networks; Problem structuring and decision attributes

objective, the study explores the possibility of developing a methodology that

promises a systematic, effective, and contextual framework to select attributes of

DRPTN models. By implementing this framework in the context of Tehran’s DRPTN,

the study meets the third objective by allowing qualified users acting as subject-

matter experts to utilize the developed framework and produce a set of decision

attributes for the DRPTN problem. Finally, this study seeks to establish a degree of

validity and evaluate to what extent this methodology was successful in serving the

purpose for which it was designed as well as the quality of the framework’s output.

1.7 Research Gap and Motivations

The DRPTN literature is enriched by valuable studies that focus on DRPTN decision-

making models that provide solutions to respond to the post-disaster failures of a

network’s elements (Karlaftis 2007). Such decision models recommend decisions

that significantly impact the life and well-being of the affected people with substantial

socio-economic, technical, and environmental cascade effects. While the quality and

reliability of these decisions depends on a comprehensive problem structuring and,

accordingly, selecting effective decision attributes, the role of problem structuring as

a prelude to the framing of a decision-making model is often neglected (Franco and

Montibeller 2010; Cochran et al. 2011). In sum, many decision-making models do not

benefit from a reproducible and transparent model that assists analysts in selecting

decision factors (Tiesmeier 2016). Thus, the task of attribute identification itself

remains a challenge that has not been adequately examined (Vaidya and Mayer 2016;

Dale et al. 2015).

The significance of problem structuring and the criticality of choosing attributes for

a decision-making model is widely evident. Problem structuring methods are already

well established in social and management sciences (Franco and Montibeller 2010);

however, engineering and construction management fields often find it a trivial task

and insignificant contribution to dedicate time and effort to problem structuring.

Particularly, in cases of disaster recovery, the certainty and representativeness of the

decision model are paramount to producing a reliable decision recommendation.

However, problem structuring and the systematic attribute selection process are

I-Introduction

often overlooked in the construction process of DRPTN decision-making models

(Zamanifar and Hartmann 2020). A common understanding has emerged in decision

modeling that a good problem formulation is one in which the existence of a unique

solution is assured in a reasonable time (e.g., Williams 2013, p., 295). Accordingly,

the degree to which the solution drawn from the decision model holds for the real

system is not seen as crucial. This mismatch between the core properties of a model

and essential characteristics of a real-world instance is even more critical when the

decision context must accommodate disaster recovery planning. As such, 77.5% of

reviewed optimized DRPTN models are formulated without a systematic approach or

a conceptual argument to support the incorporation of attributes in the decision-

making models. This observation becomes concerning when, within those studies,

efforts toward validation of DRPTN models are limited to 30% of total DRPTN

studies, and in 70% of cases, an explicit argument to support the validation phase of

the DRPTN modeling process could not be identified. Therefore, the lack of

conceptual, theoretical, or methodological underpinning for the selection of decision

attributes or to support the model’s attribute selection process is a valid concern,

since representativeness and completeness of the adopted decision parameters is the

main contributor to the quality of the decision model’s outcome. This concern has led

researchers to call for approaches that allow for a systematic and transparent

selection process of contextual and tenable decision attributes (Zamanifar and

Hartmann 2020; Ha and Yang 2018; Tiesmeier 2016; Vaidya and Mayer 2016; Dale

et al. 2015).

While some research discusses how existing attributes of decision problems are

likely subjective, intuitive, or adopted without contextual justification (e.g., Tiesmeier

2016; Xiaofei et al. 2018), it is critical for the integrity of the model that attributes are

selected based on a reliable and structured approach. The critical nature of this task

is highlighted in disaster recovery planning research due to 1) the extreme socio-

economic stakes, 2) the challenges to the validation of models due to the problem's

non-observability, and 3) the existing gap in DRPTN literature on formalizing the

attribute selection process. Additionally, DRPTN literature mainly focuses on the

problem-solving step of the decision modeling, while making insufficient effort for

Disaster Recovery Planning of Transportation Networks; Problem structuring and decision attributes

systematic formalized selecting of DRPTN attributes (Zamanifar and Hartmann

2020). In this study, we intend to flip the focus and underline the importance of

problem structuring in establishing tenable attributes for the sensitive and critical

problem of DRPTN. In the following section, the knowledge gaps and motivation for

meeting the three defined objectives are presented.

1.7.1 Motivation and Knowledge Gap in the Development of Objective 1

Over the last decade, a number of review papers addressed several disaster

management fields in both pre-event and post-event phases, covering areas such as

vulnerability, evacuation planning, emergency response, and reconstruction

planning. Among these, only a few were exclusively devoted to the recovery of the

transportation network or its functionality after disruptive events (e.g., Faturechi and

Miller-Hooks 2015; Konstantinidou et al. 2014; Abdelgawad and Abdulhai 2009;

Dehghani et al. 2013; Galindo and Batta 2013). Additionally, I could not identify a

review that investigates the problem structuring of optimization methods within

DRPTN models. Nevertheless, due to the increasing application of optimization

programming in the DRPTN context and the critical result-sensitive characteristics of

such problems, it is important to conduct such an investigation.

A review of optimization programming has been performed in many contexts.

Existing studies review the optimization methods based on how they are formulated

and solved, as well as on the context in which they are applied and how they can be

compared. While a survey of techniques used in solving or formulating optimization

problems can be viewed as common state-of-the-art optimization review studies, the

phases of validation, problem structuring, and problem identification are not the

focus. Additionally, it was not possible to identify a review reporting on the

limitations in problem structuring of optimization methods within a specific

application. When dealing with a context-sensitive problem, it is necessary to identify

the parts of DRPTN methodologies on which the quality of findings depends and, at

the same time, are not sufficiently addressed.

The existing practical knowledge on DRPTN is indeed extremely costly, if not the

most priceless one. Researchers have investigated many disasters that took

I-Introduction

invaluable lives and caused overwhelming environmental and socio-economic losses.

The outcomes of studies on disaster recovery planning provide valuable insights for

future research and measures in practice. Given that scholars have been producing

detailed seminal studies of DRPTN for three decades, it is logical that a review reflects

this valuable accumulation of knowledge and points out possible challenges and

opportunities arising in different research trends.

1.7.2 Motivation and Knowledge Gap in the Development of Objective 2

In both disaster management practice and research, insufficient effort is made to

identify contextual, representative, and complete attribute sets (Girod 2003; Belton

and Stewart 2010; Ha and Yang 2018). Attributes are often selected arbitrarily and

without contextual justification or the application of a formal approach to control for

the inevitable subjectivity associated with selecting decision factors (Tiesmeier

2016; Zamanifar and Hartmann 2020). This is perhaps because systematic

approaches toward selecting attributes and indicators are close to rare or users do

not sufficiently integrate them into the decision modeling process (Dale et al. 2015;

Niemeijer and de Groot 2006). Following a methodological approach, such as a

decision-aiding framework, is critical for ensuring the quality of problem structuring

and decision models. This is even more critical for complex problems of DRPTN due

to the socio-economic and technical consequences of decision recommendations.

Several studies highlighted that too little attention has been paid to how to obtain a

suitable list of attributes and a contextual structure among them (e.g., Maier and Stix

2013; Belton 1999; Keeney and Gregory 2005). Niemeijer and de Groot (2006)

argued that the attribute-selection process is mainly subject to arbitrary decisions

and have called for a straightforward process for selecting indicators, while Lin et al.

(2009) stated that attribute-selection processes generally suffer from being

insufficiently systematic and transparent. Moreover, Ma et al. (2016) highlighted that

answering the question of how to select the optimal decision attributes presents a

compelling future research direction, which is a critical process for many MCDM

domains. Accordingly, several researchers have called for a systematic, context-

related, step-by-step guide to act as a reliable decision-aid mechanism for attribute

selection in decision problems (Tiesmeier 2016). On this ground, to improve the

Disaster Recovery Planning of Transportation Networks; Problem structuring and decision attributes

quality of decision models in this sensitive and critical context of DRPTN, a formal

approach for establishing effective and comprehensive decision attributes is an

imperative need.

Generally, four main approaches inform the selection of attributes. The expert-based

approach refers to extracting information from stakeholders, DMs, and subject-

matter experts to articulate the important decision factors in a specific context (e.g.,

Mahdiyar et al. 2018; Hockey and Branch 1997). Literature-based attribute selection

is an adoption approach in which the selection task is based on the attributes applied

in previously conducted studies (e.g., Abidi et al. 2019; Desmond 2007). The third

approach is a combination of expert opinion and previous literature of the field (e.g.,

Kassem et al. 2016; Amer and Attia 2017). The mixed approach integrates two

available sources to develop a more comprehensive and complete set of attributes.

Finally, the systematic model-driven attribute selection approach (e.g., Otto et al.

2018; Axel et al. 2017; Dale et al. 2015; Convertino et al. 2013) presents an alternative

to overcome several challenges associated with other approaches, such as 1)

contextual adaptability of literature to the problem at hand; 2) temporal validation

and generalizability of literature-based attributes; 3) interview intensity of an

expert-based approach; 4) completeness and inclusiveness of the attribute set; 5) the

challenge of selecting from a broad list of attributes proposed by the literature and

experts; and 6) reducing the subjectivity involved in the process of attribute

selection. A model-driven approach formulates and solves the choice problem by

selecting among a finite number of attributes drawn from the literature and experts

of the field based on evaluation factors that reflect the properties of desired

attributes. Many DRPTN studies do not apply any of these approaches to attribute

selection; only 22.5% of studies exhibit arguments or a methodological set-up that

support and justify the selection process of attributes. Acknowledging the possibility

that some researchers might avoid reporting on such attempts, limitations

concerning selected DRPTN attributes, as well as the overall lack of problem

structuring in general (e.g., Belton and Stewart, 2010), provide sufficient indications

to believe that improving the approach toward the selection of attributes is worthy

of time and effort. Based on this premise, chapter three is a response to the call of

I-Introduction

several studies for a framework for identifying decision attributes (Zamanifar and

Hartmann 2020; Ha and Yang 2018; Tiesmeier 2016; Vaidya and Mayer 2016; Dale

et al. 2015).

1.7.3 Motivation and Knowledge Gap in the Development of Objective 3

Defining attributes for the problem of disaster recovery, as in any decision model, is

inherently subjective and error- and bias-prone due to the low validity decision

environment of the post-disaster DRPTN prescriptive model and the inevitable

subjectivity associated with the problem structuring (Cochran et al. 2011).

Challenges arise during the selection of attributes since epistemic and aleatoric

errors can influence the decision model’s output even if the model is mathematically

solvable and verifiable (Phillips-Wren et al. 2019; Wesley and Dau 2017; Beven et al.

2015). Furthermore, some reviews have highlighted the absence of systematically

produced attribute sets for disaster management models and pointed out their

inadequacies (e.g., Zamanifar and Hartmann 2020; Fekete 2019; Gutjahr and Nolz

2016). As a likely result of neglecting the problem structuring process, some

shortcomings concerning decision attributes were identified within the DRPTN

literature reviewed. For instance, attribute sets that address both mobility and

accessibility aspects of the modeled problem appeared only in 17.5% of the studies;

this may pose challenges to the completeness of DRPTN models. Disregarding the

topological properties of a network to measure each link's accessibility index can also

raise concerns over the representativeness of models. Similarly, only 12.5% of the

studies included the level of access to critical facilities, which shows access

restoration to service-providing nodes (e.g., medical centers, strategic nodes and

critical facilities) has not been sufficiently acknowledged. Additionally, some of the

attributes can be perceived as ambiguous such as “importance,” “urgency,” or

“capability of the repair team,” as they are too broad and qualitative to allow for a

standard, constant, and certain understanding of their definition. Furthermore, non-

operational and decomposable attributes such as “risk of recovery in sensitive areas”

or “traveler convenience” also introduce uncertainty into the DRPTN models. It is

cumbersome – if not impossible – to quantify such metrics with reasonable certainty

and operational efforts. Moreover, some DRPTN studies rely on sets that, despite

Disaster Recovery Planning of Transportation Networks; Problem structuring and decision attributes

hosting well-established attributes, introduce attribute redundancy by

simultaneously measuring related properties of the traffic performance, e.g., link

flow, link capacity, and travel time. Redundancy in attribute sets creates an

unbalanced emphasis on one objective, which adversely influences the set's

equitability. Conversely, to reach a complete set of attributes, using a relatively large

attribute set size imposes a high computational cost and uncertainty in reaching a

convergent, optimal, or compromise solution. Therefore, it is meaningful to associate

the existing challenges outlined above with the absence of a formal problem-

structuring phase in the reviewed decision models.

1.8 Research Questions

The questions below reflect three central research questions, which correspond to

the three objectives of the study. Answering these questions provided the

opportunity to address the key question of how can researchers and disaster

managers best structure the problem of DRPTN?

RQ/1: What are the challenges and opportunities in DRPTN decision modeling and

emerging improvement areas of the field?

RQ/2: How can we develop a decision-aiding framework to assist DMs in selecting

decision attributes?

RQ/3: What is an equitable set of decision attributes for the Tehran DRPTN context?

The first research question has been approached in chapter two, where I analyzed

the identified DRPTN optimization models based on four phases, including problem

definition, problem formulation, problem-solving, and model validation. The second

research question is answered in chapter three by developing a prescriptive decision

aid mechanism to assist in harnessing experts' knowledge and recommend decision

attributes. In chapter four, I addressed the third question, where I implemented the

framework in a real-world DRPTN problem case study to test its performance,

analyze the outcomes, and produce a systematically selected set of DRPTN decision

attributes.

I-Introduction

1.9 Research Methods

Within the structure of those three research papers, I adopted and developed several

methods. While in chapters two, three, and four, the research methods have been

described in detail, this section briefly present an overview of those methods.

Questionnaires were used to collect the attributes from experts, whereas content

analysis and descriptive statistics were used for the literature review. Using a

visualized slider, I collected the input of MCDM experts on the relative importance of

compensatory evaluation factors and then used an ordinal-cardinal mathematical

formulation to convert their assigned input to numerical weights. I used prescriptive

decision theory as a guide to build the attribute-selection framework as a fit-for-

purpose method and used it to identify the decision attributes of the DRPTN problem.

A focus group workshop helped to implement the framework. GIS visualization was

the means to present a disaster scenario and familiarize the DMs with the decision

environment. Direct rating point allocation helped the DMs assign numerical values

to the performance of alternatives within the evaluation process. Further, Multi-

Attribute Value Theory was selected to aggregate the DMs' inputs in the

compensatory region, while an aspect-based screening approach was used to screen

the alternatives in the screening region. Value tree concept mapping allowed DMs to

evaluate sets of attributes in the optimal region and select the set. For analyzing the

framework's output, I used retrospective comparison, information entropy analysis,

and sensitivity analysis. Finally, a semi-structured interview with a Likert scale and

an open discussion interview allowed for the collection of DMs’ feedback on the

experience of using the framework and its performance.

Table 1.2 summarizes the methods employed for performing the three tasks of

problem structuring, data collection, and data analysis within the framework of the

research design. Conceptual methods were used to frame the problem and to

establish the research design. Qualitative methods were mainly used to collect data

from DRPTN literature and experts. I then analyzed the data and the outcome of the

developed research design using quantitative methods. In the method section of

chapters two, three, and four, those methods are explained more in detail.

Disaster Recovery Planning of Transportation Networks; Problem structuring and decision attributes

Table 1.2: Adopted tools and methods for framing the research design and addressing

the three main objectives

Conceptual

Qualitative

Quantitative

Problem

structuring

- Prescriptive

decision theory

modeling

-Deductive content analysis

- Literature review

- Attribute selection

methodology

- GIS visualization and spatial

modeling

- Attribute selection method

Data

collection

- Secondary data sources

- Systematic search

- Semi-structured interview

- Brainstorming

- Survey

- Point allocation, direct rating

- Rank-based orderings

- Directed content analysis

- GIS data analysis

Data

analysis

Value tree

concept

mapping

- Content analysis

- Focus group workshop

- Descriptive statistics

- Elimination by aspect

- Multi attribute utility theory

- Cardinal rank-based

preference elicitation method

- Entropy information analysis

- Sensitivity analysis

1.10 Outline of the Dissertation

This dissertation consists of five chapters, three of which are based on published

materials in peer-reviewed journals with a focus on hazard and disaster,

transportation and resilience, and environment and decision systems. Chapter two

demonstrates a systematic, comprehensive, and critical analysis of the knowledge

gaps within DRPTN decision models and highlights challenges and opportunities in

the DRPTN modeling process. The findings presented in this chapter shape other

research questions that are answered in chapters three and four. Chapter three

responds to the gaps identified in the previous chapter and presents a set of methods

and a framework to systematically evaluate and select decision attributes. The

developed decision support framework is an attempt to formalize the process of

attribute selection. This chapter focuses on how users can apply the proposed

framework as a decision-aid mechanism for problem structuring when tackling

complex multi-criteria engineering and planning problems.

I-Introduction

Chapter four describes the process of data collection and the implementation of the

methodology proposed in chapter three in a real-life DRPTN scenario. In this chapter,

case study data is analyzed and inputted into the framework to produce a set of

decision attributes for the Tehran DRPTN decision problem. This chapter focuses

mainly on DRPTN decision attributes by providing an analysis of the resulting

attributes. The last chapter summarizes the results of this research, highlights the key

findings, elaborates on open questions, presents avenues for possible future

research, and provides practical recommendations for research and practice. This

chapter ends with a call to action to better understand challenges and opportunities

in DRPTN and the vital role of problem structuring in a decision-modeling process

that could also be generalized for other domains. Complementary contents including

research data and analyses (e.g., list of decision factors in DRPTN studies, categories

of formulated optimization problems, literature review’s parametric findings, utility

scores of attributes in the selection process, and list of attributes of the alternative

pool) that could be interesting for readers are available as supplementary materials

of papers. There are two sets of supplementary materials for chapters two and three,

which I made available on the institutional repository at TU Berlin. The links for

accessing those files are provided within the respective chapters.

Although I have tried to minimize repetition, some recapitulation was necessary to

ensure that each chapter is comprehensible on its own. Chapters two, three, and four

are papers co-authored with Timo Hartmann; therefore, I refer to “we” and “our”

while “I” is used in the rest of the dissertation. Finally, the three papers in chapters

two, three, and four have been slightly modified to better integrate them into this

dissertation and improve the overall consistency and coherence.

There are limits to this dissertation and research design, many of which I am aware,

and many I am not. However, I have chosen not to include a dedicated limitation

section in the concluding chapter. Instead, at the end of two published papers in

chapters two and three, the limitations are separately outlined. I would be grateful if

readers of this dissertation would be willing to share their critiques and comments

with me.

Disaster Recovery Planning of Transportation Networks; Problem structuring and decision attributes

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Disaster Recovery Planning of Transportation Networks; Problem structuring and decision attributes

Chapter II

DECISION MODELS FOR

DRPTN; REVIEW &

ANALYSIS

“…The problem appears hard to solve only because it is badly stated.”

Jean-Jacques Rousseau (1762), The social contract

II- Decision models for DRPTN; review & analysis

2 Decision Models for DRPTN; Review and Analysis

(Accepted Manuscript)

Zamanifar M, Hartmann T, (2020), Optimization-based

decision models for disaster recovery and reconstruction planning of transportation

networks, Journal of Natural Hazards, Vol. 104, P. 1-25, Springer.

https://doi.org/10.1007/s11069-020-04192-5

2.1 Summary

The purpose of this study is to analyze optimization-based decision-making models

for the problem of Disaster Recovery Planning of Transportation Networks (DRPTN).

In the past three decades, seminal optimization problems have been structured and

solved for the critical and sensitive problem of DRPTN. The extent of our knowledge

on the practicality of the methods and performance of results is however limited. To

evaluate the applicability of those context-sensitive models in real-world situations,

there is a need to examine the conceptual and technical structure behind the existing

body of work. To this end, this paper performs a systematic search targeting DRPTN

publications. Thereafter, we review the identified literature based on the four phases

of the optimization-based decision-making modeling process as problem definition,

problem formulation, problem solving, and model validation. Then, through content

analysis and descriptive statistics, we investigate the methodology of studies within

each of these phases. Eventually, we detect and discuss four research improvement

Contributions: The first author had the idea and performed the literature search, data analysis,

drafting the discussions, and result development. The second author proposed the structure, supervised,

contribute to improving the discussion and communication of the paper as well as series of edits and

proofreads. The second author also revised the paper.

Disaster Recovery Planning of Transportation Networks; Problem structuring and decision attributes

areas as 1] developing conceptual or systematic decision support in the selection of

decision attributes and problem structuring, 2] integrating recovery problems with

traffic management models, 3] avoiding uncertainty due to the type of solving

algorithms, and 4] reducing subjectivity in the validation process of disaster recovery

models. Finally, we provide suggestions as well as possible directions for future

research.

2.2 Introduction

We define the decision-making model for Disaster Recovery Planning of

Transportation Network (DRPTN) as a prescriptive decision model, constructed to

respond to an extreme hazard that i) exhibits structural damages on the transportation

network’s components. ii) Directly causes major operational disruptive impacts on the

traffic functionally of the network or part of it and iii) can be alleviated only by physical

construction interventions such as repair, and reconstruction operations. The existing

studies on DRPTN develop decision-making models in which road’s components have

to be prioritized for reconstruction such that it optimizes predefined objectives (e.g.,

Lertworawanich 2012; Kaviani et al. 2018; Shiraki et al. 2017). As a tool, optimization

modeling is embedded in Decision Support Systems that formulates and solves

problems involving (often) multiple conflicting objectives (e.g., Zhu et al. 2019; Xu et

al. 2019; Xing 2017). Particularly, in the setting of the transportation network, as a

highly critical and intricately interwoven infrastructure, optimized decisions are

products of optimization-based decision modeling that recommend solutions

responding to the post-disaster failures of a network’s elements (Karlaftis 2007;

Zamanifar and Seyedhoseyni 2017). While many reviews investigate the application

of optimization modeling in different contexts and fields, it is close to rare in disaster

recovery context yet ever-growing essential. This necessity lays on the fact that

optimization-based decision modeling, as goes for many complex decision analyses,

is an error-prone task that chiefly relies on modelers’ judgment (Phillips-Wren et al.

2019; Winter et al. 2018; Beven et al. 2015). This inevitable subjectivity could result

in committing the error of the third kind to either correctly solve a wrong problem

or partly solve the right one (Mitroff and Featheringham 1974). Besides, the

II- Decision models for DRPTN; review & analysis

criticality and sensitivity of the disaster recovery problem exponentially escalates the

consequence of errors in DRPTN models. This criticality and sensitivity are due to the

cascading impact of disasters in urban areas that propagates on a wide scale and

emerges beyond the damage of physical assets to adversely affecting people,

economy, environment, and social systems (Kadri et al. 2004). Another reason is the

inherent characteristic of disaster recovery problems due to its non-observability as

there is sparse matching data of disasters that can be compared with the output of

developed DRPTN models for the evaluation purpose (Sargent 1996 and 2011; Day

et al. 2009; Kadri et al. 2014). Even if data is partly available, performing a

retrospective test to validate a model is a cumbersome task, if not impossible, due to

the degree of inconsistency between two datasets of the previous and probable

future disasters (Leskens et al. 2014; Celik and Corbacioglu 2010). The non-

observability of a problem emphasizes the pressing need of particular care for

defining, formulating, and solving prescriptive models that represent critical and

sensitive real-life problems. Hence, it is logical to recognize the need for clear

identification of possible uncertainty sources and vulnerable parts of DRPTN models

that may challenge the validity and quality of the outcome (Buchanan et al. 1998).

To this end, the objective of this paper is to evaluate existing optimization-based

DRPTN models’ components to identify and discuss the challenges that can provide

understanding toward improving the accuracy and practicality of optimization-based

DRPTN models. Additionally, since the focus of existing reviews on optimization

modeling is mainly on solving algorithms, we performed our analysis based on four

phases of optimization modeling as problem definition, problem formulation,

problem solving, and model validation (Nocedal and Wright 1999; Horst and Tuy

1996; Williams 2013). This bottom-up approach helps us to review the performance

of an optimization model based on its components such as decision factors, choice

variables, solving techniques, objective functions, and result analysis methods.

Accordingly, the task of problem definition and identifying decision factors is the first

phase of optimization decision-making modeling. The second phase is to formulate

the problem such that it demonstrates the representative properties of the modeled

problem. In this step, analysts set up relations among decision factors and variables

Disaster Recovery Planning of Transportation Networks; Problem structuring and decision attributes

and then translate them into mathematical equations. In the problem-solving phase,

the selection and implementation of a matching and robust solving approach is the

concentration to maintain the quality of the model and the feasibility of outcomes

simultaneously. The last phase is to verify and validate the model’s output such that

one can apply it as a reliable solution to a real-life problem. Accordingly, to analyze

the identified papers, we first studied the problem definition of DRPTN models to

explore the adopted decision factors of models and approaches toward selecting

those factors. In the problem formulation phase, we tried to understand as to how

relationships among objectives are set and how this relationship can be

contextualized for the problem of DRPTN. Furthermore, we investigated the phase of

problem solving in the reviewed DRPTN literature by identifying the rationale for

adopting problem solving algorithms based on objective functions, complexity, and

convexity of problems. Finally, we studied the model validation phase to identify

approaches toward evaluating the performance of the DRPTN models and the

developed mathematical algorithms.

As a review strategy, we began with a systematic search to identify relevant

publications based on DRPTN definition and accordingly multiple terms that address

hazards, disasters, recovery, roads, and transportation networks. We then used the

content analysis approach for analyzing the existing literature. Doing so, we first

divided and structured the optimization modeling process into four phases.

Afterward, we extracted the information from the reviewed texts that address the

adopted phases. Once the representative contents of each publication were

categorized, we identified the elements of models that were consistent in all

publications such as decision factors, solving techniques, number of objective

functions, validation efforts, and so forth. We applied two review questions as 1)

What methodological elements of DRPTN models could challenge the validity and

contextual application of models’ outcomes? 2) How the rationales for structuring the

four phases of optimization modeling are conceptually supported? Based on the

review questions, we developed several comparing matrixes to state the relation

between extracted elements that may lead to possible limitations in the

methodologies of DRPTN research. We detected and discussed four research

II- Decision models for DRPTN; review & analysis

improvement areas as the findings of this study which are: 1] developing conceptual

or systematic decision support in the selection of decision factors and problem

structuring, 2] integrating recovery problems with traffic management models, 3]

avoiding uncertainty due to the type of solving algorithms, and 4] reducing

subjectivity in the validation process of disaster recovery models. The identified gaps

point out important areas of optimization modeling in the context of disaster

recovery that could contribute to the improvement of DRPTN models’ performance.

The paper presents a contextual understanding of the construction process of DRPTN

models which provides insights for decision-makers as to what can be expected from

the existing models’ performance and what uncertainties they could take into

account while receiving decision recommendations of an optimization-based DRPTN

model. The study could be also useful for decision analysts and scholars who intend

to employ optimization modeling in disaster recovery planning applications.

Within the last decade, a number of review papers addressed several disaster

management fields in pre-event and post-event phases such as vulnerability,

evacuation planning, emergency response, and reconstruction planning. Among

those a few were exclusively devoted to the transportation network and its

functionality after disruptive events (e.g., Faturechi and Miller-Hooks 2015;

Konstantinidou et al. 2014; Abdelgawad and Abdulhai 2009; Dehghani et al. 2013;

Galindo and Batta 2013). However, despite outstanding findings, to the best of our

knowledge, addressing the recovery and reconstruction phase of the transportation

network was not the focus of those studies. Meanwhile, the literature review on

optimization programming is relatively common in different contexts. Existing

reviews analyze the optimization methods based on their formulation approach,

solving technique, the application of solvers in a specific context (e.g., Fernandes et

al. 2018; Wu et al. 2018; Udy et al. 2017; Marler and Arora 2004). While there exist

valuable information on the application of optimization solving algorithms, we chose

to look at optimization programming as a process. This approach is particularly

essential for disaster recovery context because the representativeness of the

formulation and reliability of a model’s outcome depends on an accurate problem

structuring and methodological approach within all four phases of optimization-

Disaster Recovery Planning of Transportation Networks; Problem structuring and decision attributes

based decision modeling (Belton and Stewart 2010). Additionally, we failed to

identify a review that investigates the adaptability and problem structuring of

optimization methods within DRPTN models. Nevertheless, such an effort is of great

importance due to the increasing application of optimization programming in the

DRPTN context and critical result-sensitive characteristics of such problems.

2.3 Optimization-based Decision-Making Models and DRPTN

Optimization is designing or identifying the most favorable choice among a set of

alternatives subjected to a set of formalized bounds (Bertsekas 2015). It consists of

one or multiple objective functions and a set of variables as well as a defined set of

constraints in a finite non-empty subset of a partially ordered space. An optimization

model eventually specifies a possible set of non-dominated solutions by varying the

selection or order of variables that represent an optimal compromise among

objectives (Ehrgott 2005). Variables are alternatives that diverge to optimize

objective functions also called choice set or unknowns (Nocedal and Wright 1999).

Constraints refer to the applicable limits on decision choices and are responsible for

articulating the functional relationships among alternatives. They also allow users to

express enforced behavior of a system and indicate certain limitations. A general

form of an optimization problem can be shown as Φ(𝑘,𝑥)=

{max [𝑓1(𝑥),… 𝑓𝑛(𝑥)]|Φ (𝑘′,𝑥)} where 𝑓𝑖(𝑥) is the objective function and Φ (𝑘′,𝑥) is known

as the constraints. A multi-objective problem in optimization modeling refers to the

notion that the optimal solutions for more than one objective are different and

changing the values of the decision vector to improve one objective might result in a

decrease in the value of other objectives. Accordingly, Pareto optimality expresses

achieving a set of ideal solutions that indicates the optimum trade-off among those

conflicting objectives.

For solving an optimization model, problem complexity is an important concept.

Problem complexity identifies how difficult it is to achieve the optimal solution for an

optimization problem. This difficulty is measurable with the required computational

resource that a solving algorithm consumes until it terminates on the optimal or

near-optimal solution. The resource is usually referred to the running time (time

II- Decision models for DRPTN; review & analysis

complexity) or the used memory (space complexity). When some problems exhibit

close asymptotic behavior in consuming computational resources for obtaining

optimal solutions, then they shape a class of complexity. Insights from the

computational complexity of problems especially tackling non-convex problems can

locate the cumbersome part of the formulation, which indicates where it is possible

to aggregate, decompose, or simplify and helps to model the problem effectively

(Tovey 2002).

As an inherent property for some classes of optimization problems, every local

optima is a global optima. These problems are referred to as convex optimization

problems (Bertsekas 2015). Informally, convexity in optimization means that

objective functions and feasible sets formed by constraints shape a convex feasible

region that ensures the existence of the global minimum. Convexity analysis refers to

the evaluation of the geometric feature of the feasible region toward constructing

smooth convex objective and constraints functions. Detecting the convexity of the

feasible region of the problem provides useful insights to assimilate the complexity

of the problem and eventually selecting an efficient solving algorithm (Johannes

2013). As Figure 2.1 illustrates, presuming that the right problem is recognized, we

present the optimization modeling as a process with four main phases namely

definition, formulation, solving, and validation. The following section introduces the

properties of each phase and its importance in the context of DRPTN.

Disaster Recovery Planning of Transportation Networks; Problem structuring and decision attributes

Figure 2.1: Phases of decision-making modeling and steps of optimization programming

2.3.1 Problem Definition

Modeling of a real-scale problem aims at abstracting the perceived system and the

problem in one environment (Phillips 1984). It initiates with identifying the problem

and selecting its decision parameters as part of problem structuring (Keeney 1992).

In optimization-based decision-making modeling, the problem’s components are the

decision factors, which express the system’s function, and decision variables that

control the behavior of decision parameters. Among decision factors, attributes

evaluate the performance of the system and the distance to the desired state of the

system articulated by objectives. Though decision-making models eventually

optimize the given objective functions, quality of the resulting outcome depends on

“the completeness of the model in representing the real system” (Taha, 2007).

Meanwhile, representing the real system is highly contingent upon defining decision

factors such as objectives and attributes (Belton and Stewart 2012; Keeney and

Gregory 2005).

There are many well-posed optimization problems with clearly defined decision

parameters such as production efficiency problem, manufacturing problems,

blending problems (Zopounidis and Doumpos 2002). However, in the disaster

recovery planning context, problems do not often emerge clearly labeled or with fully

II- Decision models for DRPTN; review & analysis

defined properties. In the aftermath of a disaster, objectives and preferences are

dynamic and hardly recognizable (Leskens et al. 2014; NRC 1999). Additionally,

effective attributes and even in some cases alternatives are vague as well. Hence, a

thorough investigation of the problem definition step as the preliminary phase of the

optimization modeling process is vital. Even more so in the context-dependent and

critical problem of DRPTN that is highly complex and cannot afford conceptual error

in representing the real system due to a broad impact of results on multiple accepts

of a big scale society. On this ground, we study the variety of attributes that DRPTN

studies developed and analyze the rationale for choosing those attributes.

2.3.2 Problem Formulation

This phase formulates a mathematical translation of the defined problem and

establishes sets of relationships among variables and decision factors (Morris 1967).

When modelers achieved an equitable set of decision factors in the problem

definition phase, in this phase they seek the desired arrangement among them

(French 2018; Williams 2013). Additionally, selecting the target set of variables of

the problem is a task of this step since those variables are part of possible solutions

that ultimately shape the feasible region of the optimization problems (Ehrgott 2005;

Lange 2013). Although this step has many interrelations with the phase of problem

definition, since both are parts of the problem structuring, yet it cannot proceed

unless the outcome of the first step is available. Unlike problem definition during

which modelers select decision parameters, in the problem formulation phase, they

decide as to how to treat decision parameters. Problem formulation, additionally,

deals with integrating the target variable sets and assign values to objective functions

to achieve a meaningful and formalized mathematical expression of the intended

problem.

In doing so, traffic assignment simulation is a common sub-model for assigning value

to traffic decision factors of optimization models in transportation planning. Traffic

assignment models simulate the traffic on a network based on origin-destination

travel demand to identify the traffic flows distribution on links on which equilibrium

is obtained. There are two general approaches for traffic assignment: System

Optimum and User Equilibrium (Wardrop 1952). The System Optimum traffic

Disaster Recovery Planning of Transportation Networks; Problem structuring and decision attributes

assignment approach assigns the traffic flow to links in order to optimize the ideal

possible traffic distribution on the whole network. In contrast, User Equilibrium

distributes the traffic flow on the network to reach equilibrium on links based on the

utility of routes and the assumption of rationality of drivers (Wardrop 1952). DRPTN

optimization problems mainly design the order of variables to optimize the value of

traffic assignment models next to other objectives.

In planning for a transportation network, physical assets such as bridges, highways,

or links are common choice variables. Administrative or non-physical components

are also variables that either represent or impact the performance of the

transportation network such as traffic calming strategies, rerouting plans, options of

lane management, and travel demand regulations. Problem formulation, in DRPTN,

usually adopts the physical components as a variable set to prioritize the recovery

tasks of those components that optimize an objective or the trade-off between

multiple objectives. These objectives represent different problems after a disaster

such as relief distribution, resource allocation, or network design problem. Basically,

each problem is associated with its specific choice set variables, which are configured

next to the transportation network’s components. For example, relief distribution

problem adds relief units to the variable of the optimization model or the problem of

resource allocation incorporates available work teams and budget into the

computation. The integration between those problems eventually constitutes the

final variable set as well as the configuration among them to compute the objectives.

This integration in DRPTN is critical because, on one hand, the statement of an

optimization problem is affected by the nature of relations among decision

parameters. On the other hand, a practical multi-facet problem of DRPTN needs to

address the goal of modeling by incorporating effective objectives. This motivated us

to investigate the problem formulation phase to understand variables and the

problem integration within DRPTN models.

2.3.3 Problem Solving

Solving an optimization problem could be the simplest step of optimization modeling

because it entails the use of well-defined optimization algorithms and tools (Taha

2007). Nevertheless, selecting an efficient, robust, and fitting technique that promises

II- Decision models for DRPTN; review & analysis

a reliable optimal solution is a challenging part of solving DRPTN problems. In that

context, deterministic and non-deterministic algorithms are the main approaches

toward finding solutions for optimization problems. Deterministic algorithms return

exact minima points of the solution space. Examples of these algorithms are;

Sequential Quadratic Programming, Generalized Reduced, Gradient, and Dynamic

Programming. Non-deterministic approaches are heuristic and meta-heuristic

population search, evolutionary or trajectory search, and their extensions that lead

to methods such as Genetic Algorithms, Simulation Annealing, Particle Swarm,

Harmony search, and Tabu Search (for a review see e.g., Blum and Roli 2003). These

algorithms provide feasible but not necessarily optimum solutions and cannot

submit a mathematical proof of whether the returned configuration is minimal or at

least how good it is compared to the optimum solution (Schneider and Kjrkpatric

2006; Talbi et al. 2012). Having that in mind, when the degree of complexity and size

of a problem increases, deterministic algorithms consume an unreasonable amount

of computational resources. It means solving a big-size non-convex NP-hard problem

in polynomial time would be extremely difficult (unless NP=P). In this case,

employing a non-deterministic method is a logical choice that relatively easily

handles such a problem with the effort that grows polynomially as do the size of the

problem. Therefore, while many problems have been solved with deterministic

approach, meta-heuristic optimizers are popular attacking engineering and complex

problems.

Although the mathematical procedure of solving DRPTN problems with non-

deterministic methods is generally correct, the validity of a solvers’ outcome cannot

be properly examined (Festa 2014; Rardin and Uzsoy 2011) as it operates as a black-

box solver and without any further problem-specific adjustments (Rothlauf 2011).

Context-independent, general-purpose, or black-box solvers cannot explore the

structural properties of the objective function. A feature of these algorithms is that

the outcome solution might be inferior to purpose-specific algorithms that solve the

same problem (Marti and Reinelt 2011).

This is a major concern when researchers develop sophisticated algorithms to solve

mathematically modeled DRPTN problems while the rationale behind the selection

Disaster Recovery Planning of Transportation Networks; Problem structuring and decision attributes

of the optimization methods remains unevaluated, especially in the sensitive

problem of DRPTN that exact result is vital for reliable planning engaging with human

life. Therefore, in the context of DRPTN uncertainty due to the utilizing solving

algorithm can be a challenge when multiple objective functions are involved in the

modeled problem (Liefooghe 2011; Horst and Tuy 1996; Talbi et al. 2012).

Particularly, uncertainties and biases due to the quantification of values or assigning

preferences (e.g., in priori decomposition-based approaches) also question the

validity of solutions since epistemic uncertainty can easily propagate to the

optimization output (Limbourg 2005) even when the model is mathematically

correct. Therefore, it is logical to investigate the impact of objective level in DRPTN

models on the accuracy of results and rationale behind utilizing solving algorithms in

DRPTN models. In this study, the objective level refers to the number of objective

functions that a model intends to optimize. Single-objective optimization problems

contain one objective function and the bi-objective level problem refers to problems

with two objective functions that usually formulate a leader-follower game. Similarly,

models that are formulated with three and four objective functions are identified as

multi-objective. When a model seeks to optimize more than four objective functions,

it forms a many-objective problem.

2.3.4 Model Verification and Validation

Model validation and verification are two concepts toward irrespectively evaluating

the reliability of a model’s outcome and quality of the solution. Model validity

indicates how well the optimal solution of the model is to solve the real-life instance

of the intended problem. Model verification, however, demonstrates how well the

output represents intended developed mathematical relationships among

parameters (Oberkampf et al. 2003; Oberkampf and Roy 2010; Sargent 2011).

Validation is a process that attempts for obtaining sufficient confidence (if there can

be any) that the solution of the model can be considered valid for its intended

application. The classical approach of validation is based on comparing the outcome

of the model with the known experimental measurement of the same problem in

reality when the input set for both systems are equivalent (Roy and Oberkampf 2011;

Sargent 1996).

II- Decision models for DRPTN; review & analysis

Validation in the context of DRPTN is challenging because the confidence threshold

in models is set relatively high since DRPTN-related decisions are associated with

human life and enormous socioeconomic losses. Additionally, disaster recovery

problems are highly prone to epistemic and aleatoric uncertainties as well as

parametric errors due to the complexity, context-dependency, and time-stretched

process of the decision-making. Therefore, the “value of model to user” dictates the

demand for maximized model confidence (Sargent 2011). Existing optimization

models for disaster recovery problems deliver fast and efficient solutions while they

might be limited in representing many of the crucial realities of the modeled system.

In such a situation, the validation of models is an imperative phase of the modeling

process to evaluate the quality of the model. It answers the question of whether the

result can be trusted as bases for making decisions in a critical engineering

socioeconomic situation (Babuška et al. 2007). To provide a better understanding of

the significance of this question we investigate the validation and verification efforts

within DRPTN models.

2.4 Review and Analysis Methodology

2.4.1 Search Strategy

We performed a systematic literature search to find optimization studies that

addressed disaster recovery planning for damaged transportation networks. Based

on our earlier definition of DRPTN, we established certain exclusion and inclusion

criteria to design clear boundaries for the literature search. The four main criteria

were, first, the candidate publication studies a component of a transportation

network. Second, the system disruption of the study occurred due to a hazard or a

large-scale disruptive event. Third, the target of papers is to present a recovery,

reconstruction, or repair planning for damaged elements. Fourth, studies use

optimization modeling to develop the problem. The search task was according to

various terms addressing disaster and transportation network in the abstract, title,

and keywords of the publications. We repeated the search task with different terms

representing the same concept. For example, addressing the term disaster, we

performed the search with terms such as “disaster”, “hazard”, ”extreme event”,

Disaster Recovery Planning of Transportation Networks; Problem structuring and decision attributes

“earthquake”, “landslide”, “emergency” “flood”, and “tsunami”. Similarly, for the

transportation network, we searched for ‘’transportation’’, ”traffic”, ”bridge”, ”link”,

”road”, ”highway”, and ”network”. Thereafter, we discarded duplicate publications as

the outcome of multi-platform searching and sifted the searching process by limiting

disciplines as well as exclusion of irrelevant keywords. Selected disciplines were

business, management and accounting, computer science, decision sciences, earth

and planetary sciences, engineering, environmental science, mathematics, and

multidisciplinary.

Reducing errors in finding related publications, we tried to strictly follow our

designed benchmarks. Additionally, we agreed not to use multiple screening or

filtering steps presented by the used platforms. Instead, we chose to manually

investigate the final set of references (n= 910) based on three steps of content

analysis to learn whether the publications belong to the scope of our study or not.

These steps were irrespectively content analysis of a) abstract, b) abstract,

methodology or problem description section and c) full-text of the publications

(n=241). Moreover, we also used the snowball method by performing a forward

referencing search in the selected papers’ reference lists that has led us to identify

three additional publications.

2.4.2 Content Analysis

The content analysis is based on analyzing the methodology of DRPTN studies

following the phases presented in sections 2.3.1. to 2.3.4. We evaluated the studies

with respect to possible sources of uncertainties and conceptual vulnerabilities in the

formulation, problem structuring, problem solving, and validation process of DRPTN

decision-making models. For this purpose, we performed a directed content analysis

and measured the number of studies for all extracted information based on Figure

2.2. We framed two review questions to approach the publications as 1) What

methodological elements of DRPTN models could challenge the validity of models’

outcomes? 2) How the rationales for structuring the four phases of optimization

modeling are conceptually supported? Figure 2.2 shows the detailed steps of the

content analysis framework that we describe in the rest of this subsection.

II- Decision models for DRPTN; review & analysis

Figure 2.2: The systematic review and gap analysis flowchart for the literature of DRPTN

In the first step, we extracted the elements of the methods applied to our content

analysis strategy and the framework of optimization decision-making process

introduced in section 2.3. Doing so, we analyzed various components of

methodologies such as decision attributes, formulation approaches, solving methods,

convexity and computational complexity analysis, arguments supporting the

selection of solving methods and the selection of attributes as well as model validity

and verification arguments. The second step focused on performing multiple

identification and grouping of optimization components including objective counts,

attribute types, employed traffic performance metrics, problem integration types,

types of solving algorithms, and types of variable sets. For example, we categorized

the attributes within three main classes of emergency, traffic, and economic.

Accordingly, the traffic factors include attributes that represent the performance of

the transportation network such as travel time, capacity, or density. Emergency

factors are attributes that respond to the social and individual urgent needs after

disasters and demonstrate the performance of emergency response operations such

as relief distribution, housing, or population. Lastly, economic factors represent the

budget and cost-related attributes incorporated in the planning such as direct or

Disaster Recovery Planning of Transportation Networks; Problem structuring and decision attributes

indirect damage costs.

After that, we developed several comparing matrixes to state the relation between

extracted elements that may lead to possible limitations in methodologies of DRPTN

research as: numbers of objectives and used solving methods, complexity class

arguments and used non-deterministic algorithms, formulation approaches and

integrated problems, as well as traffic engineering methods and the application of the

post-disaster travel demand. Also, the analysis included the corresponding presented

theories and methodologies for establishing attributes, selecting solving algorithms,

and developing validation approaches in each study. Finally, we analyzed the

frequency of the detected gaps to report challenges that are overall in the body of

DRPTN literature. Accordingly, the next section presents the results of performing

content analysis in the reviewed DRPTN literature.

2.5 Findings

This section demonstrates the findings of the content analysis in each phase of

DRPTN optimization modeling process.

2.5.1 Problem Definition

Figure 2.3 shows the attributes that DRPTN models employ. Additionally, Table 2.1

demonstrates the types of attributes and their combinations that are categorized

according to whether they focused on emergency, traffic, or economic goals.

Figure 2.3: Attributes employed in DRPTN as well as their categories.

II- Decision models for DRPTN; review & analysis

Table 2.1: Amount and share of attributes in three categories as well as their combination

within DRPTN studies (Em: Emergency, Tr: Traffic and Ec: Economic factors)

Figure 2.3 and Table 2.1 show that most DRPTN studies establish traffic attributes to

measure the technical performance of networks such as mobility and level of service.

In some cases, a combination of traffic attributes represents an attribute for network

functionality. Figure 2.3 shows that Travel time is the most frequent attribute to

measure the quality of the traffic service after disasters and Travel flow appears in

41% of the studies. Furthermore, two studies (5%) adopt Travel distance and five

studies (10%) incorporate Travel demand and link Capacity to measure the

achievements of their objectives. With respect to economy attributes, in the whole,

19 studies (47.5%) consider budget-related attributes such as Direct cost, which

simply refers to the repair cost of transportation components. Six publications (15%)

additionally apply Indirect cost which in four studies was associated with the direct

cost. Indirect cost represents the economic disruption due to network failure or

secondary costs due to the travel delay. In total, nine studies (22.5%) combine

economic and traffic attributes in their models.

Emergency attributes address critical civil needs after disasters or represent metrics

that can influence the risk of fatality. For example, Relief demand as a major attribute

in this category in seven studies (17.5%) refers to traffic nodes to which emergency

supply should be distributed. Five studies (12.5%) incorporate the attribute of

Emergency facilities for links that provide access to those nodes. Six studies (15%)

consider Population in a traffic zone or Population that is served by links to addresses

an emergency aspect of the post-disaster situation. Furthermore, 16 studies

introduced emergency attributes and five studies (12.5%) incorporate attributes to

measure the social impact of disasters on an urban area. Finally, based on Table 2.1,

five papers (12.5%) develop the attribute sets with all three categories of decision

factors.

Factors

Em/Tr/Ec

Em/Ec

Em/Tr

Ec/Tr

Counts

Share (%)

97.5

47.5

12.5

2.5

17.5

22.5

Disaster Recovery Planning of Transportation Networks; Problem structuring and decision attributes

Lastly, we analyze the content of DRPTN studies to identify information or

approaches that support the selection of attributes. In this regard, 22.5% of the

studies provide conceptual arguments to theoretically support this selection or

identification. For instance, Feng and Wang (2003) provide a section to identify

objectives of the planning, recovery characters, resource constraints, and decision-

making process to accordingly justify the selection of the attributes. In another case,

performance attributes by Unal and Warn (2018) “… were selected to be

representative and to facilitate the restoration design based on available data and

reasonable computational efforts” and was supported by specific details for each

parameter and importance of the selection.

2.5.2 Problem Formulation

To investigate the formulation approach of DRPTN optimization problems we

analyzed the integration of objectives, sets of choice variables as well as objective

value assignment approaches in traffic flow distribution models. Table 2.2 shows the

choice variable sets of optimization DRPTN models.

Table 2.2: The alternative variable sets of optimization models within DRPTN

Within the transportation network’s components, DRPTN models regard bridges,

railways, routes, segments, links, and nodes as variables. These physical components

form the alternative set of 97.5% of models, of which 25 studies (63%) integrated

Variables

Coun

(%)

Note

Components

37.5

Bridge, railway, link. route, segment, node

Components and resources

27.5

Integration of two sets of alternatives

Sequence of recovery of

components

17.5

Including sets that are combined with resource

choices

Set of components

7.5

Strategic or zone-based solution set

Sequence of components and

resources

7.5

Links and contractors/ work troops

Sequence of assigning resources

2.5

Relief units

II- Decision models for DRPTN; review & analysis

transportation network’s components with other variables. Table 2.3 shows the

integration of objectives and consequently sub-problems within DRPTN.

Table 2.3: Integration of post-event problems with the recovery problem

Task

Count

(%)

Recovery and network design

27.5

Recovery and task scheduling

22.5

Recovery and resource allocation

Recovery

Recovery and relief distribution

DRPTN models identify resources such as budgets, work troops, and contractors, but

always in combination with physical components (except for one study that uses

resources independently). 11 studies (27.5%) focus on sequences of alternatives to

optimize recovery activities with respect to all possible orders among alternatives.

Furthermore, three studies (7.5%) adopt sets of components as the variables defined

by selected recovery strategies or a network zone.

Four studies (10%) formulate a model of relief distribution and recovery problem

with integrating variables and objectives of both problems. This problem integration

prioritizes the recovery tasks that timely meet the post-event needs or optimizes the

aid distribution process by solving a network routing problem. Nine studies (22.5%)

formulate tasks of scheduling and recovery problems in one optimization model to

assign the recovery tasks to contractors and optimize the traffic performance of a

network against cost or duration of the recovery. This formulation also optimizes

multiple metrics of the network subjected to scheduling constraints such as material

or machinery limitations. Resource allocation and recovery problem integration (8

studies, 20%) optimizes the sequence of recovery activities for minimizing the

budget or reconstruction duration while maximizing a technical metric of the

network. Also, some models assign resources to a sequence of recovery projects in

which a compromise between technical objectives of the network and reconstruction

cost can be found. 11 studies (27.5%) formulate the integration of network design

Disaster Recovery Planning of Transportation Networks; Problem structuring and decision attributes

problems and recovery problems to prioritize recovery tasks according to the

network traffic load. These studies propose the use of traffic assignment on a

degraded network to identify the importance of specific links. In addition, the

network design problem can indicate the optimized recovery order that reduces the

travel time for emergency vehicles.

Finally, 23 studies (57.5%) formulate the decision models based on the output of

traffic assignment models that assign quantified value to the objective functions.

Therefore, we investigated the traffic assignment approach within DRPTN models, to

understand how DRPTN models are formulated to address post-disaster travel

demand of the network. Accordingly, two studies (5%) modify the regular travel

demand for the post-disaster condition addressing limitations in the functionality

and accessibility of the network. Additionally, except for one paper that considers the

System Optimum approach, User Equilibrium traffic assignment is the dominant

approach for assigning traffic flow to the network.

2.5.3 Problem Solving

75% of the DRPTN models (30 studies) use non-deterministic algorithms in the

problem solving phase such as Genetic Algorithm, Simulated Annealing, Tabu search,

and Ant Colony. To understand the rationale of selecting non-deterministic

algorithms and the impact of this selection on the quality of outcomes we investigate

the objective level of optimization problems that are solved by non-deterministic

methods. Additionally, we analyze the arguments that support selecting non-

deterministic methods to solve the optimization problems. Figure 2.4 shows the

relation between objective numbers and the rate of studies that used non-

deterministic methods for solving the intended problems in each class of objective

count.

II- Decision models for DRPTN; review & analysis

Figure 2.4: The use of single, bi, multi, and many objectives formulation in DRPTN

research and percentage of used non-deterministic methods in each objective level.

Non-deterministic algorithms solved 54% of the problems with one defined objective

function. Similarly, 73% of the problems with two and 89% of the problems with

three and four objectives are solved by non-deterministic methods. Figure 2.4 also

shows that problems with one and two objective functions reach 67.5% of the whole

DRPTN optimization models and one study developed the optimization model with

more than five objective functions. Furthermore, Table 2.4 provides an overview of

the rationale that DRPTN studies reported for choosing non-deterministic

optimization methods.

Table 2.4: Description and amount of discussions over applying non-deterministic

algorithms in optimization problems.

Count

The argument for utilizing the non-deterministic methods

No discussion presented

23.3

NP-hard according to characteristics discussed by other sources

16.7

Due to computation cost

6.7

Computation complexity discussed

3.3

Avoiding Braess’s paradox (Braess 1968)

Nine papers (30%) address the complexity of the problem. Two of those studies

(6.7%) fully discuss the class of complexity of their optimization problems and seven

studies (23.3%) identify a known Hard problem within the original problem which

results in an NP-Hard or Complete problem thus accordingly derive the methodology

toward utilizing non-deterministic methods. Furthermore, three publications (10%)

point out the convexity state of their problem although without a report of an

investigation over visualized geometric of the search space or computing the Hessian

Disaster Recovery Planning of Transportation Networks; Problem structuring and decision attributes

matrix for the second-rate derivative of the objective function. Additionally, five

studies (16.7%) mention the computational cost of solving methods as the reason for

selecting non-deterministic algorithms, although no representative computational

indication could be identified.

2.5.4 Model Validation

In the validation phase of the optimization decision-making models, some DRPTN

studies provide approaches and arguments to assess the quality of algorithms and

models while in the majority of cases we failed to identify explicit argument on the

validation phase of the developed models. Table 2.5 and Table 2.6 demonstrate how

reviewed DRPTN studies evaluate the performance of algorithms and validate the

solution of models and to what extend studies did not offer a direct argument

referring to the validation phase of DRPTN models.

Table 2.5: Efforts and arguments toward verifying and validating DRPTN models.

Arguments on validation of the models

Case

Count

Numerical case for validation

Validation is left for future studies

No specific argument is provided

Table 2.6: Efforts toward verifying solving algorithms of DRPTN models

Efforts on evaluating the performance of the algorithms

Case

Count

Numerical example

Sensitivity analysis

27.5

Algorithms computational performance

Algorithms verification tests

No effort identified

27.5

Results show that eight publications (20%) represent their numerical examples as a

validation approach for the developed model. Also, ten studies (25%) provide

numerical examples to conclude the performance or quality of the developed

II- Decision models for DRPTN; review & analysis

algorithm. For example, a study states that the reason for providing a numerical

example is “to verify the feasibility and applicability of the method” and claims are

made that […] it also indicates that this method is clear, efficient and adaptive and it

can provide theoretical foundation and technical evaluation” (Yuan et al. 2014).

Another case highlights that the numerical example “…proves the validity of models

and algorithms, provided a scientific foundation for the government to make

reasonable rush-repair scheduling when the disasters occur” (Zhang and Lu 2011). On

the other hand, some studies directly point out that the presented application

example “... is to illustrate the use of programming formulation …” (Orabi et al. 2010)

or to only “…evaluate the algorithm’s performance…” (Wang et al. 2011) within the

model. For example, Sato and Ichii (1995) present a numerical example to test the

efficiency of the solving algorithm and Duque and Sörensen (2011), el Anwar (2016),

or Hackl et al., (2018) emphasize that experimental future works are required for

validation of the model.

Furthermore, 18 studies (45%) evaluate the algorithm’s computational performance.

Additionally, eight studies (20%) employ standard verification tests to evaluate the

mathematical performance of their models such as consistency tests, simplified

testing, output comparison with similar models, and comparison with all permutated

results (in small size problems). Finally, 11 publications (27.5%) analyze the

sensitivity of variables and weight vectors aiming at assessing the performance of

models.

2.6 Discussion and Suggestions

Based on the findings of the previous section, we provide arguments for the identified

challenges and opportunities within each phase of the DRPTN optimization

modelling process.

2.6.1 Problem Definition

The broad set of attributes within DRPTN offers divers and exhaustive

representations of the real system which itself is diverse and stochastic. At this stage,

practice can benefit from various problem definitions DRPTN literature provides to

Disaster Recovery Planning of Transportation Networks; Problem structuring and decision attributes

address different and specific real-world problems. Equally important, DRPTN

models have the potential for improvement in enhancing the completeness of the

attributes set. One of the reasons is the absence of highly effective attributes in the

decision factor sets of some DRPTN models. For instance, although the transportation

network disaster recovery is a technical problem, it serves a social system (Nigg

1995; Lubashevskiy et al. 2017). Nonetheless, only five studies incorporate social

vulnerability or an indicator that measures the social impact of recovery operations.

Additionally, the expected outcome of a disaster recovery model in practice is to

alleviate the calamitous impact of disasters on societies given its sociotechnical

aspects. Nevertheless, the main goal of DRPTN studies is set to improve only the

technical performance of the road network, since 95% of studies incorporate traffic

attributes and 50% of them introduced their model only based on traffic attributes.

Furthermore, only five sources (12.5%) include all three clusters of decision factors

and seven studies (17.5%) introduced a combination of traffic and emergency factors

in their formulation.

Additionally, the interaction of a transportation network’s components with other

critical infrastructure networks (lifelines) is a widely acknowledged critical decision

factor in disaster management (Zhang 1992; Cavalieri et al. 2012; Kadri et al. 2014).

Nevertheless, we could not find this factor in any of the reviewed studies as an

attribute toward optimizing recovery activities. Lifeline interaction is an important

attribute for prioritizing the recovery of links since early-stage damage control in

other interconnected infrastructures such as the gas delivery network or power lines

is essential to avoid secondary, technical, and cascading hazards. Similarly, only

12.5% of the studies included the level of access to critical facilities, which shows that

“accessibility” and, in particular, access restoration to service providing nodes such

as hospitals, fire stations, strategic points, control centers, or shelters have not been

considered sufficiently yet.

A worth noting finding is that in the majority of the reviewed DRPTN studies (31

studies, 77.5%), we could not identify a systematic approach or a conceptual

argument to support the incorporation of attributes in the developed decision-

making models. This argument is also consistent with the identified challenge by

II- Decision models for DRPTN; review & analysis

some studies in different fields (Ha and Yang 2018, Tiesmeier 2016, Fekete 2019).

However, we are not able to pinpoint the cause, yet, the absence of incorporation of

highly effective attributes such as accessibility and social factors within the attribute

set of DRPTN models might be the result of the absence of a formal or informal effort

to identify effective decision factors.

To control subjectivity and reduce conceptual errors in establishing decision factors,

we suggest the development of a systematic framework toward the selection of

decision factors in the DRPTN context. To avoid the error of the third kind, it is

critically important that such efforts recognize the collectivity of the disaster

recovery problem. It is a necessary task that future studies address the identification

of complete and collective sets of decision factors or establish accredited evaluation

criteria for such a set. Accordingly, a broad descriptive and qualitative analysis of the

problem in the initial steps of research and dedicating more time and effort into the

problem conceptualization and problem structuring is inevitable.

2.6.2 Problem Formulation

DRPTN studies addressed essential post-disaster problems by integrating different

objectives in one decision environment such as relief distribution, route planning,

and resource allocation. As a whole, DRPTN studies cover many variables of the post-

disaster setting. Meanwhile, DRPTN models formulate representative properties of

the post-event network performance regardless of administrative variables.

Additionally, the problem formulation of DRPTN models might be challenging in

terms of contributing to post-disaster traffic quality in surviving networks with the

recovery schemes. This interpretation is apparent based on Tables 2.2 and 2.3, as we

could not identify studies that integrate disaster recovery planning and traffic

management problems. Nor could we identify a study that adopts traffic management

measures such as redistribution of the traffic flow, rerouting, signals management,

lane reversal, temporary shoulder capacity, etc., as an administrative variable set of

the DRPTN optimization problem.

Regarding the representativeness of DRPTN models in the formulation phase, the

status quo of DRPTN studies is using the assumption that post-event traffic flow

Disaster Recovery Planning of Transportation Networks; Problem structuring and decision attributes

follows a sub-pattern of the existing pre-event traffic flow along some degree of

network geometric restrictions (damaged nods or links). This assumption is

understandable due to the high degree of uncertainty and complexity in predicting

the route choice of travelers after a disaster that within DRPTN exists a lack of

interest in estimating the post-disaster traffic condition of networks since User

Equilibrium is the most popular approach within DRPTN models. However, this

might be a too simplified assumption since, on one hand, User Equilibrium

philosophy is based on the reflection of the optimal state of each traveler according

to his or her perception in a normal condition and perfect information environment.

In addition, according to Braess’s paradox (Braess 1968), the equilibrium is not

necessarily relaxing in the ideal state of the network. On the other hand, in the

significant information lack condition of the post-disaster environment (Day et al.

2009), the route choice utility (Dobler 2011), serviceability of the system (Chang and

Nojima 2001) and even users of the network (Iida et al. 2000) are radically different

from the pre-event condition. On this ground, User Equilibrium cannot realistically

represent many features of traffic flow in the post-event distributed network since

several fundamental assumptions of this approach are violated in the post-disaster

traffic behaviors. Accordingly, the findings suggest the challenge of formulating

DRPTN models in assigning representative values to objective functions as well as

integrate traffic management variables with recovery options.

To improve the DRPTN formulation, applying the User Equilibrium approach for the

post-disaster phase can be revised by manipulating variables and the problem

integration. Doing so, we suggest shifting the role of traffic assignment from a post-

event unknown variable to a known target value, i.e., design the optimization

problem such that the model finds the optimized order of variables to reach the ideal

given state of the network in the Service Optimum approach. This formulation also

entails including traffic management measures as an auxiliary alternative set next to

the recovery activities. Using integrated traffic management and recovery planning,

planners can assist and direct the users’ route choice in the post-event phase. This

formulation approach optimizes travel demand of the ideal traffic flow distribution

by designing a new network plan based on the surviving network, recovery options,

II- Decision models for DRPTN; review & analysis

and updated administrative regulations (e.g., lane reversal, demand regulation signal

management). It can indicate how external interventions by planners after a disaster

(recovery of links and traffic management) lead the network toward reaching the

optimum equilibrium based on the Service Optimum traffic assignment approach.

2.6.3 Problem Solving

The incorporation of non-deterministic algorithms within the problem of DRPTN in

many cases overcomes the challenge of solvability of DRPTN problems. In fact,

DRPTN studies could very effectively harness the advantages that non-deterministic

methods offer. Therefore, it is impossible to ignore the benefits of fast and feasible

solutions of non-deterministic algorithms, however, results also suggest the

challenge of conceptual and computational support for selecting the solving method

as well as the absence of complexity and convexity analysis before choosing the

algorithms. Figure 2.4 shows the increase in employing non-deterministic algorithms

when the number of objectives rises. Accordingly, a compromise between certainty

and effectivity is apparent within DRPTN models. The more objectives do models

incorporate, the less certain the final solution is. On the contrary, the more solving

algorithms try to yield an accurate mathematical outcome; the model can cover fewer

objectives. Thus, it might exhibit a lack of inclusion to address various aspects of a

post-disaster condition. The compromise between certainty and effectivity arises

since; a) subjectivity and errors within the process of selection and quantification of

decision parameters and b) the urge for use of non-deterministic algorithms due to

the complexity of a problem, both cardinally grow with the number of objectives

(Vianna and Vianna 2013; Limbourg 2005). This is a challenge for the quality of multi-

objective optimizations when a result-sensitive context-dependent problem is solved

with a context-independent method with no guarantee of returning optimal results

at the global level (Ishibuchi et al., 2008). This challenge is highlighted when 73% of

bi-objective and 54% of single-objective problems have been solved by non-

deterministic algorithms even though the exact methods are generally valid for single

and bi-objective optimization problems up to a large size (Vianna and Vianna 2013;

Liefooghe 2011). Consequently, although the increase in objective numbers provides

a more contextually exhaustive and effective model to cover different dimensions of

Disaster Recovery Planning of Transportation Networks; Problem structuring and decision attributes

a disaster recovery problem, it also comes at its impact on the certainty of the

algorithm’s solution. Therefore, given the critical engineering socioeconomic nature

of DRPTN problems, the right balance between exactness of result and inclusion of

the model is a critical consideration that might require broader attention to the

problem-solving phase of DRPTN optimization modeling process. To reduce

uncertainty in solving disaster recovery problems, it perhaps would make more

sense to utilize non-deterministic methods only for optimization problems with

multiple objectives and constraints that even their approximation apt to be a

cumbersome task.

Besides the absence of convexity analysis, it is believed that “the complexity class of

an optimization model dictates the nature of the solving method” (Taha 2007). Yet,

53.3% of studies chose the solving method regardless of complexity investigation of

the problems and only two studies present a detailed discussion on complexity

analysis of the problems. Moreover, although it is commonly understood that when a

problem is NP-Hard then non-deterministic methods are the method of choice, the

fact is ignored that many NP-Hard problems can be still solved relatively fast with

standard mathematical methods (Rothlauf 2011). Therefore, it is logical to consider

both complexity class and convexity analysis of DRPTN problems before choosing the

solving algorithm since when an optimization problem formulates a convex problem,

it is very likely solvable deterministically and efficiently (Boyd and Vandenberghe

2004; Grötschel and Holland 1991). On this ground, while solving a critical result-

sensitive problem of DRPTN, an important consideration is that approximation is

secondary to the deterministic approach as long as an exact solution is achievable.

However, complexity class and convexity analysis of the DRPTN models have not

been sufficiently emphasized. Among 50% of the reviewed studies, we failed to spot

conceptual or computational justification that supports the application of non-

deterministic algorithms for a specific problem, even though the size of the problem,

in most of the cases, was relatively small and the number of objectives in 67.5% of

cases was not exceeding two. Therefore, we suggest that future research evaluate the

complexity class and convexity state of the problems of interest before choosing a

solving method, As Rockafellar (1997) highlighted, “The familiar division between

II- Decision models for DRPTN; review & analysis

linearity and nonlinearity is less important in optimization than the one between

convexity and non-convexity” (Rockafellar 1997). Another suggestion is to consider

formulation approaches which likely form a convex solution space such that exact

methods can solve the problem. As an instance, we can highlight the work of el-Anwar

et al., (2016a and b) which formulates a mix-integer optimization problem with a

convex cone in the DRPTN context and could efficiently improve the near-optimal

solution to the optimal solution.

2.6.4 Model Validation

Despite the non-observability of DRPTN problem, the fact that 72.5% of studies

conducted efforts to systematically evaluate the outcome of the models indicates that

within the field of DRPTN the awareness is established that the DRPTN problem is

highly result-sensitive thus cannot afford inaccuracy in the solution and requires a

relatively high level of confidence. At the same time, results point out a potential

improvement area in validating disaster recovery models. That is because, based on

the classical definition of the model validation, (which relies on the comparison of a

known solution to the model’s outcome), efforts toward validation of DRPTN model

are limited to 30% of total DRPTN studies and in 70% we were not able to identify

explicit argument to support the validation phase of DRPTN models. Alternatively,

we observed that eight studies (20%) provide hypothetical numerical examples to

validate their models. However, an illustrative example might not provide sufficient

evidence to conclude the validity, quality or applicability of the entire model because

it is tested within a simplified network and based on several uncertain assumptions,

stochastic input data, subjective values and preferences, scenario-based damage

states, and static traffic distribution. Scenario-based numerical case studies (with

real-world data) can provide some level of confidence in the mathematical

configuration of algorithms and are beneficial in the sense of invalidating the model

that initiates the advancement of the model construction in each invalidation process

(Popper 1987). Using terms such as “effective”, “validated”, “accredit” for evaluating

developed models based on internal properties of a model can yield misleading

expectations from the model for future research and users of a publication in the

sensitive critical context of DRPTN (Konikow and Bredehoeft 1992).

Disaster Recovery Planning of Transportation Networks; Problem structuring and decision attributes

Furthermore, 11 studies (27.5%) conduct a sensitivity analysis to evaluate the

performance of models. Sensitivity analysis is indeed necessary to evaluate the input-

dependency of the model as an observation over the internal behavior of the

objective function to a supervised change in variables or weights. However, this

observation, might offers very little in terms of insight or foresight about the validity

of models to indicate its reliability to be used for a real-world instance of the indented

problem (Oberkampf et al. 2003; Babuˇska and Oden 2004; Scandizzo 2016). Because

sensitivity analysis neither evaluates the validity of the information fed into a model

nor assesses the validity of the defined conceptual relationship among the models’

parameters. Nevertheless, sensitivity analysis can sophisticatedly determine the

degree of robustness of the model, logical relationships, or verify the algorithm.

Therefore, although performing sensitivity observation is essential for DRPTN

models, it should not be used interchangeably as a mechanism for the model

validation in the DRPTN context.

A pressing need for the DRPTN field is to develop frameworks and approaches within

the modeling process that provide a level of confidence in DRPTN models and

pinpoint clear benchmarks within the validation process. One of these measures is to

distinguish between subjective and objective parts of the models and control the

subjectivity in the steps of the model construction. Another suggestion is to develop

a set of critical conditions, tests, and boundaries in an attempt to refute DRPTN

models or to quantify the uncertainty associated with the result of the model.

Moreover, producing accredit synthetic observed data can also facilitate the

“comparison of a known data to the known solution” that allows obtaining a

satisfactory degree of credibility of models. This approach provides data from a

simulated real world that can be compared to models’ predictions. It, therefore,

worth initiating efforts toward simulating a comprehensive visualized multi-

dimensional, multi-disciplinary, agent-based post-disaster environment that can

capture the complexity of the system and allow users to directly evaluate the

consequences of different optimized recovery strategies.

II- Decision models for DRPTN; review & analysis

2.7 Summary and Conclusion

As a summary, first, we observed that DRPTN studies provide diverse sets of

attributes in different categories, however, in a significant amount of cases, no

conceptual underpinning has been presented to justify or support the selection

process of the model’s attributes. Therefore, it is essential that future studies propose

systematic bias-reduced methods and methodologies toward establishing the

attribute set of DRPTN problems and conduct a solid problem structuring. Second,

despite successful divers formulations of the recovery problem, we could not identify

an integration of traffic management and the disaster recovery problem and

including traffic management options as a variable set of the decision model next to

recovery projects. Hence, we proposed to integrate variables of route reopening and

traffic control measures to reach the optimized performance of the transportation

network. Third, we concluded that DRPTN problems require a computational,

conceptual, and context-dependent justification for the selection and application

sense-making of the solving methods. Therefore, we suggest devoting more effort to

the identification of local characteristics of the problem with respect to complexity

and convexity as a technical justification of utilizing deterministic and non-

deterministic methods. Obviously, aiming at global solutions in the DRPTN context, if

there were any, would promote the reliability of the model. In the last section, the

study identified the major focus on verification of the optimization algorithms.

Developing a systematic approach to provide a degree of confidence in the quality of

non-observable models’ solution remains a compelling direction for future works.

Accordingly, the field of disaster recovery of infrastructures is calling for high-

resolution simulations of the urban system in a microscopic level that facilitates

modeling the individual decision-making process, within its sub-models and

assimilates the user-user and user-system interactions in the post-disaster scenarios.

Finally, we pose this question that whether we need more novel, fast, and feasible

optimization algorithms regardless of their conceptual and methodological strength

in supporting the rationale of models’ elements. Rather, research directions that can

introduce science-developed-but-practice-oriented models which provide error-

minimized practical results for operational levels. Perhaps what the field of DRPTN

Disaster Recovery Planning of Transportation Networks; Problem structuring and decision attributes

needs is not a new optimization approach or solving technique but conceptual

descriptive models and systematic frameworks that stand as a solid foundation for

models’ construction and structuring (Landry et al. 1983) in problem definition,

solving and validation phases to avoid a method-rich but methodology-poor

phenomenon in the optimization-based DRPTN context.

II- Decision models for DRPTN; review & analysis

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Disaster Recovery Planning of Transportation Networks; Problem structuring and decision attributes

Chapter III

A METHODOLOGY FOR

SELECTION OF

ATTRIBUTES

“If a tractable model is obtained, enrich it. Otherwise, simplify.”

William T. Moriss, On the art of modeling, (1967).

III- A methodology for selection of attributes

3 A Methodology for Selection of Attributes

(Accepted Manuscript)

Zamanifar M, Hartmann T, (2021), A prescriptive decision

model for selecting attributes of infrastructure risk reduction problems, Environ Syst

Decis 41, 633–650 (2021). https://doi.org/10.1007/s10669-021-09824-0

3.1 Summary

This paper proposes a framework to systematically evaluate and select attributes of

disaster recovery decision models. In doing so, we formalized the process of attribute

selection as a sequential screening-utility problem by formulating a prescriptive

decision model. The aim is to assist decision-makers in producing a ranked list of

attributes and selecting a set among them. We developed an evaluation process

consisting of ten criteria in three sequential stages. We used a combination of three

decision rules for the evaluation process, alongside mathematically integrated

compensatory and non-compensatory techniques as the aggregation methods. We

implemented the framework in the context of disaster resilient transportation

networks to investigate its performance and outcomes. Results show that the

application of the framework acted as an inclusive systematic decision-aiding

mechanism and promoted creative and collaborative decision-making. The

Contributions: The first author developed the idea and the framework as well as related mathematical

models. Furthermore, he established the discussions based on the framework's performance, analysis of

results, and drafting the paper. The second author proofread, and commented on the structure and

communication of the paper. The second author also participated in the revision of the paper.

Disaster Recovery Planning of Transportation Networks; Problem structuring and decision attributes

properties of the resulting attributes and feedback of the users suggest the quality of

outcomes compared to the retrospective attributes that were selected in an unaided

selection process. Further analyses are required to discuss the performance of the

produced attributes. Both research and practice can use the framework to conduct a

systematic problem-structuring phase of decision analysis and select an equitable set

of decision attributes.

3.2 Introduction

Decision analysis is used for planning and solving problems concerning

environmental challenges, which often integrate multiple objectives and decision

attributes. When responding to risks in environmental systems such as climate

change and natural hazard-induced disasters, several objectives and attributes are

involved covering multifaceted characteristics of a modeled problem. Identifying the

underlying decision attributes is an essential, preliminary step in the decision-

making modeling process (Keeney 2007; Belton and Stewart 2012). However, in both

practice and research, systematic approaches towards the selection of attributes are

either rare or inadequately applied which hinders the identification of contextual,

representative, and complete attribute sets (Dale et al. 2015; Niemeijer and de Groot

2006, Tiesmeier 2016). Attributes are often selected without the contextual

justification or formal approach needed to shift speculative intuitions to rational

judgments (Tiesmeier 2016). This issue has been shown in many decision-making

contexts, including Disaster Recovery Planning of Transportation Network (DRPTN)

(Zamanifar and Hartmann 2020). DRPTN is a decision-making context in which

optimized recovery operation plans are identified. These operations respond to the

disruptive impact of hazards to restore an expected performance of a transportation

network with repair and reconstruction operations. The extent to which the

outcomes of DRPTN decision models are effective and reliable relies on the quality of

attributes integrated into the decision modeling process. Therefore, selecting tenable

decision attributes is critical for complex and sensitive disaster recovery problems

due to the socio-economic and environmental consequences of decisions (Sandri et

al. 2020; Beling 2013). However, a gap in conceptual or systematic support for the

III- A methodology for selection of attributes

selection process of DRPTN attributes exists. Based on this premise, the current

paper is a response to the call of several studies for an approach that allows a

systematic and transparent selection process of contextual decision attributes

(Zamanifar and Hartmann 2020; Ha and Yang 2018; Tiesmeier 2016; Vaidya and

Mayer 2016; Dale et al. 2015). On this ground, we propose a framework in the form

of a decision aid mechanism that supports and facilitates the selection of attribute

sets. In doing so, we formalize the process of attribute selection as a screening-utility

choice problem, since “the problem of choosing between various formulations can

itself be represented as a complex decision-making problem” (Mitroff and

Featheringham 1974). As part of the developed framework, we formulated a

prescriptive multi-criteria decision model. The model incorporates ten criteria as the

evaluation factors based on the literature of Multiple-Criteria Decision Analysis

(MCDA) and a combination of compensatory and non-compensatory techniques as

the aggregation and evaluation method. We used this model in three sequential

stages of evaluation to assist decision-makers (DMs) in assessing the performance of

both attributes in isolation and attributes in sets. Once the framework was developed,

we tested it in a real case problem of disaster recovery planning and analyzed the

results together with the application process of the framework.

Although the framework (supposedly) possesses the capacity to be generalized to

various decision contexts, mainly one that addresses complex environmental

planning problems, we chose to explore its performance in the context of recovery

planning of transportation networks after environmental hazards. On this ground,

we collected decision attributes from the literature of DRPTN and experts’ opinions

as the input of the model. Then, we held a workshop with experienced emergency

managers as the DMs for conducting the evaluation of inputted attributes following

the flowchart of the framework. Results suggest that the framework is capable of

facilitating a degree of supervision over the selection process and promoting critical

and creative thinking. DMs were able to systematically evaluate attributes and

collaboratively produce a ranked list and a set of attributes. The implementation of

the developed framework revealed satisfactory application from the users’ point of

view. Based on the entropy information analysis of evaluation factors, DMs of the case

Disaster Recovery Planning of Transportation Networks; Problem structuring and decision attributes

problem were more inclined to select “understandable” and “certain” attributes for

the at hand disaster recovery problem. We employed several analyses, including

typological examination of the set, properties of the selection process, and the

feedback of experts, to investigate the quality of the attributes while further

experimental evidence is required to support the attributes’ performance.

3.3 Knowledge Gap and the Necessity

As a representation of values in a decision context, attributes clarify the meaning of

objectives and measure the consequences of different alternatives (Keeney and

Gregory 2005). The attribute set of a decision model represents essential problem-

related characteristics and the behavior of the modeled system (Keeney and Gregory

2005). The degree to which this representativeness is preserved within attributes

indicates the directness of attributes. A primary purpose for establishing a set of

attributes is to disaggregate a complex decision problem into more analytically

tractable components while maintaining the representativeness and collectivity of

the modeled problem as direct as possible. Therefore, a well-thought-out attribute

set can increase the likelihood of representativeness, directness, and completeness

of a decision model. Despite the critical and fundamental role of attributes in decision

analysis, the inadequacy of problem structuring and efforts for attributes

identification in the decision modeling process is well documented (see, e.g., von

Winterfeldt and Fasolo 2009; Tiesmeier 2016; Belton 1999). Maier and Stix (2013),

Belton (1999), and Keeney and Gregory (2005), among others, raised awareness that

far too little attention has been paid to the manner in which a list of attributes and

their contextual structures are obtained. Specifically, much of the literature on

decision analysis neglects the role of problem structuring and thorough

investigations on attributes as the primary task for structuring a decision-making

model (Franco and Montibeller 2010). Similarly, in practice, Girod et al. (2003)

observed that during three workshops involving experts engaged in the decision-

making process of an engineering design, less than 8% of the time was used to

identify the criteria for the targeted problem (Girod et al. 2003). Thus, it is hardly

clear to what extent the model recommended solution holds for the real system

III- A methodology for selection of attributes

(Corner et al. 2001). This issue is crucial for Decision Support Systems (DSS) in

disaster recovery and environmental models that seek to present decision-making

methodologies associated with tremendous socioeconomic loss or gain (Goujon and

Labreuche 2015; McDaniels et al. 2015).

A destructive or disruptive event in urban area that hinders access within a

transportation network or adversely influences the safety and efficiency of a

network’s mobility, to any extent or period that exceeds the affected community's

socioeconomic tolerance and coping capacity, can be perceived as a disaster.

Consequently, the concept of resilience is employed to mitigate, postpone, or

eliminate the likelihood of a hazard transforming into a disaster. Resilience is "the

‘shear zone’ between (dynamic) adaptation and (static) resistance" (Alexander

2013). More specifically, disaster resilience in the transportation network context

refers to plans and actions that improve the recovery potential of network

performance and adapt to the network's failure during and after a disaster. Non-

resilient transportation infrastructure leads to significant economic loss, threatens

society's health and well-being, and exacerbates the consequence of hazard exposure

and vulnerability (Kurth et al. 2020; Koks et al. 2019). To increase resilience,

developing reliable disaster recovery planning is essential to meet the restorative,

rapidity, redundancy, and resourcefulness properties of resilient infrastructures

(Bernau 2003; Liu 2020). Recovery planning of a transportation network is an

essential characteristic for a disaster resilient community, usually formulated as a

decision model to rank or optimize links or recovery operations (Zhang et al. 2017;

Aydin et al. 2018; Rouhanizadeh and Kermanshachi 2019). To improve disaster

recovery planning, one must establish a set-up in which DMs can make informed

decisions concerning the attributes integrated into the disaster recovery decision

model. Therefore, it is of utmost importance that disaster recovery models harness

the benefit of properties of a desirable attribute set while engaging with such ever

evolving and critical problems (Pearson et al. 2018; Quigley et al. 2019).

Studies have pointed out the role of MCDA in the decision modeling processes used

for risk assessment, resilience, and recovery planning (e.g., Cegan et al 2017; Rand et

al. 2020; Manyaga et al. 2020). Keisler and Linkov (2014) highlight the utility and

Disaster Recovery Planning of Transportation Networks; Problem structuring and decision attributes

favorability of MCDA, such as linear additive scoring models in decision

recommendations for environment models. Rand et al. (2020) argue that disaster

recovery planning requires decision models and decision support systems for

informed decision-making since the recovery of infrastructure is coupled to at-risk

communities' resilience. While the application of MCDA in prescriptive decision

models is evident, it has also been vastly employed for problem structuring,

identifying decision values, or relevant metrics under the guide of frameworks (e.g.,

Fox-Lent et al. 2015; Convertino et al. 2013; Linkov et al. 2018). For example, Linkov

et al. (2013) developed the Resilience Matrix framework to identify metrics where

performance scores for critical functions related to disaster resilience of a defined

system can be calculated. Keeney and McDaniels (1992) highlight that a key

component in decision analysis is the use of facilitation to identify values and frame

the multi-criteria problem (Keeney and McDaniels 1992). Moreover, Keisler and

Linkov (2014) also argue that the value of interventions in decision analysis is not

only in the scoring and rating of alternatives but the ability to facilitate discussion

and articulating viewpoints and decision values. They further point out a need for

tools and approaches to allow analysts to measure and discuss the desirability of

hypothetical alternatives. This paper seeks to offer a facilitation process that helps

DMs process values in a certain decision context and to more reliably select decision

attributes. The necessity of this facilitation escalates when the decision context

embeds disaster resilience and recovery planning.

Whilst the critical importance of attributes is generally recognized, it is still

insufficiently addressed in the disaster risk management context. DRPTN studies

have introduced a wide range of attributes to optimize or rank recovery operations

of lifelines, whilst only 22.5% of studies have illustrated how the problem of DRPTN

is structured or decision attributes are selected (Zamanifar and Hartmann 2020).

Even with highly visible decision processes, insufficient thought is typically given to

the identification and choice of attributes (Keeney and Gregory 2005), while in the

context of DRPTN, variables and factors are often inherently uncertain. This

challenge is not limited to the disaster management field, but has been shown in other

contexts too. For instance, Desmond (2007) outlines that there is a lack of

III- A methodology for selection of attributes

methodology to assist in identifying attributes or alternative sets in the strategic

environmental assessment field. Similarly, Ha and Yang (2018) share the same point

of view and recognize this gap in the infrastructure performance assessment domain.

They highlight that studies lack a systematic approach capable of processing and

incorporating adequate information, such as decision factors, into the decision

problem. Furthermore, Niemeijer and de Groot (2006) argue that the selection

process of attributes is mainly subject to arbitrary decisions and called for a clear

process for selecting attributes, whilst Lin et al. (2009) believe that attribute

selection processes in most cases are insufficiently systematic and transparent.

Tiesmeier (2016) identifies the same shortcoming in the real estate domain, reported

incomplete lists, as well as high inconsistency across studies while identifying

attributes. He underscores that very few studies fully justify the adoption of the

chosen attribute systems. Moreover, Ma et al., (2017) highlight that answering the

question of how to select the optimal decision attributes is a compelling future

research direction and a critical process for many domains that use decision analysis.

Fekete (2019) takes a similar stance and emphasizes the demand for guidance on

attribute selection in disaster social vulnerability context. Overall, many decision-

making models fall short in benefiting from a reproducible and transparent model

that assists analysts in selecting decision factors (Tiesmeier 2016). That is, the task

of attribute identification itself remains a challenge that has not been adequately met

(Vaidya and Mayer 2016; Dale et al. 2015) which has led to a call for a systematic

guide as a reliable decision aid framework to select attributes of decision problems.

3.4 Current Approaches towards the Selection of Attributes

Excluding the arbitrary selection of attributes, studies choose attributes based on

expert opinions, literature, or a combination of the two. The expert-based approach

refers to drawing out information from stakeholders, actors, and DMs to articulate

important decision factors in a specific context (e.g., McIntosh and Becker 2020;

Elboshy et al. 2019; Mirzaee et al. 2019). The expert-based approach has the benefit

of being based on the experiences of experts who possess the knowledge related to

the values of the decision context (assuming that the desired properties of

Disaster Recovery Planning of Transportation Networks; Problem structuring and decision attributes

stakeholder analysis, interviews, inclusion criteria of interviewees, and aggregation

methods are met). However, on the one hand, it falls short in including existing

literature and might fail in providing a complete list of attributes. On the other hand,

expert opinions are assumed reliable sources for providing preferences and values in

a decision-making process as long as they possess adequate decision-relevant

knowledge, experience, or stake (Bond et al. 2008). Nevertheless, numerous

empirical studies suggest that individuals’ striking inability to understand their

objectives, values, and preferences, and their markedly deficiency in communicating

them is a plausible consideration (Bond et al. 2008; Barron and Barret 1996;

Kahneman et al. 1982). Thus, expert-driven attributes could be a product of bias and

error-prone efforts in a limited amount of time and lesser in-depth thinking on a

specific problem (Girod et al. 2003; Tiesmeier 2016). In order to shift towards a less

interview-intensive and intuitive approach, some studies used the available

literature to identify and select the attributes of a decision problem (e.g., Herrera and

Kopainsky 2020; Merad et al. 2019; Yu and Solvang 2017). Although selecting

attributes based on existing literature is an accepted approach, critique holds that

literature might disregard some aspects of a problem due to its limitations in

accessing comprehensive data, simplifying assumptions, and communication. When

one adds the challenge of dynamic nature of problems, temporal limitation of

empirical studies, and the contextual inconsistency of literature-recommended

attributes, therefore, sole reliance on existing literature might not sufficiently ensure

an exhaustive and error minimized approach for selection of attributes. To shape a

more complete, up-to-date, and practical set of attributes, the third approach is a

combination of expert opinion and previous literature within the field (e.g., Walpole

et al. 2020; Caruzzo et al. 2020; Kassem et al. 2016). While this approach maximizes

the exhaustiveness of the inclusion of attributes, it yields a broad list of attributes

from which some must be selected intuitively. Nevertheless, objectively supervise

this intuition to select a viable attribute set remains a challenge. Thus, a prescriptive

model as a decision intervention is needed to formulate and solve the choice problem

of the selection among a finite number of alternatives.

To overcome this challenge, the model-based approach has been introduced as an

III- A methodology for selection of attributes

alternative to systematically select effective attributes that cover the concerns and

values of the problem under consideration. Accordingly, a few studies provide model-

driven attributes by formulating the selection process of attributes as a choice

problem (Cinelli et al. 2020; Höfer et al. 2020; Otto et al. 2018; Axel et al. 2017; Dale

et al. 2015; Convertino et al. 2013). Regardless of the source of the alternative pool,

these studies evaluate candidate attributes based on properties of the desired

attribute and apply a systematic process to select the attribute set. Properties of the

desired attribute are factors that evaluate the merits of an attribute such as

unambiguous, operational, and direct (see, e.g., Keeney 1992). Our work extends this

strand of approaches with some innovation in the formulation approach, capability,

and generalizability of the application. First, as a general guide for constructing a

framework that seeks to prescribe a decision, we followed the recommended

structure of the prescriptive decision analysis. Prescriptive decision analysis is an

intervention process to model a rational choice with the recommended steps of

problem structuring, preference elicitation, evaluation/aggregation, and solution

handling (Clemen 1996; Kenney 1982). Second, we introduced three stages of

evaluation that lead us to three decision regions and subsequently three decision

rules. The multi-stage evaluation process allows the incorporation of ten evaluation

factors without the urge of introducing hierarchy into the criteria system or

increasing the complexity of the modeled problem. This architect of the evaluation

environment also leads to a thorough yet cognitively manageable evaluation process.

Third, the built-in screening evaluation stage grants the inclusion of candidate

attributes from various sources such as literature and expert opinions. Fourth, the

developed decision model not only evaluates attributes but also evaluates sets of

attributes in the third decision region. Fifth, we proposed a comprehensive and

illustrated framework to support the implementation of the decision model that can

be used for future research and practice as well as by those who are not necessarily

an expert in decision analysis. Therefore, the added value of this research is:

1. Formulating the process of selecting attributes of the DRPTN problem as a

prescriptive decision model to aid the attribute selection process and DMs’

knowledge acquisition;

Disaster Recovery Planning of Transportation Networks; Problem structuring and decision attributes

2. Exploring the performance of integrating compensatory and non-

compensatory decision rules and introducing a new application for this

integration;

3. Presenting a tractable and user-friendly framework to assist systematic multi-

stage evaluation and selection of tenable decision attributes of disaster

recovery planning problems.

The framework aims to systematically process the DMs’ inputs to contextual decision

values and assist them in selecting an effective, operational, and complete set of

decision attributes. The contribution of this paper is the proposed framework and the

embedded decision model. The practical implication of results is to help decision

analysts to make an informed choice and tenable decisions within the construction

of a decision-making model. Therefore, scholars who develop multi-objective or

multi-attribute decision models can use this framework in the problem-structuring

phase of their modeling process.

3.5 Evaluation Factors and the Decision Environment

As decision criteria, we adopted existing evaluation factors of attributes, or

“properties of a good attribute” (Keeney 1992), by conducting a review in MCDA

problem structuring literature. Based on the recommendation of Franco and

Montibeller (2010), these evaluation factors are adopted to address whether

attributes are operational and relevant to the decision context, the way they measure

the performance of alternatives, and how they are aligned to the objectives. In the

literature, except for Roy (1996), the properties of an attribute and a set of attributes

are not distinguishably discussed. Therefore, we took into account the “properties of

a good set of attributes” by identifying the factors that address the characteristics of

an attribute set. We also interpreted “measurability” to “certainty of measure” to

tailor a set of evaluation factors for our particular problem, since we had good

reasons to believe that after a disaster, the certainty of the measuring associated with

an attribute reduces the uncertainty of the value of an objective. Table 3.1 shows ten

adopted evaluation factors, where seven count for members of an attribute set while

three factors evaluate sets of attributes.

III- A methodology for selection of attributes

Table 3.1: The evaluation factors for members of an attribute set and sets of attributes

suggested by MCDA literature

Evaluation factors

For members

For set

Suggested by

Coherency with

objectives

◆

Belton 1999; Majumder 2015; Gregory and Falling

2002

Operational

◆

Baker et al. 2001; Belton 1999; Dodgson et al. 2009;

Belton and Stewart, 2012, Keeney, 2007

Discriminative

◆

Baker et al. 2001; Gregory and Falling, 2002

Understandable

◆

Keeney 2007; Belton and Stewart 2012; Roy 1996

Direct

◆

Belton and Stewart 2012; Majumder 2015

Certainty in measure

◆

Gregory and Falling 2002; Majumder 2015

Representativeness

◆

Roy 1996; Baker et al., 2001; Dodgson et al., 2009;

Belton and Stewart, 2012; Keeney, 2007

Completeness

◆

Belton and Stewart, 2012; Dodgson et al., 2009; Roy,

1996; Baker et al., 2001

Non-redundant

◆

Belton and Stewart, 2012; Dodgson et al. 2009; Baker

et al. 2001; Roy 1996; Gregory and Falling 2002

Concise

◆

Belton 1999; Majumder 2015; Gregory and Falling

2002; Baker et al. 2001

Evaluation factors are divided into three decision regions based on whether they

evaluate the performance of individual attributes or a set of attributes, and whether

they address the property of necessary or sufficient conditions of the desired

attribute. That led us to three decision regions for which we assigned each a known

decision rule: compensatory, non-compensatory, and optimal. The reason for

designing a multi-stage evaluation strategy is to take into account both the properties

of evaluation factors and properties of alternatives of this specific problem.

Therefore, while in the first two regions, attributes are evaluated individually, in the

third region, they are evaluated as a set. For the properties of evaluation factors, the

first region includes factors that are necessary for attributes to meet. Hence,

compromise among factors is not desired which justifies the use of non-

compensatory decision rules. The second decision region includes factors that can

compensate for each other, which makes using a compensatory decision rule

reasonable. In the third decision region, the optimal performance of three evaluation

factors is the target of the evaluation. Additionally, designing separate decision

regions allowed us to reduce the complexity of the evaluation process and avoid

possible errors and biases that could come with a hierarchized criteria structure such

Disaster Recovery Planning of Transportation Networks; Problem structuring and decision attributes

as systematic spitting bias (Hämäläinen and Alaja 2008) influence of the type of

asymmetry in a hierarchy (Marttunen et al. 2017), and larger variance in weights

(Jacobi and Hobbs 2007). Breaking the evaluation into three discrete stages resulted

in a more cognitively manageable process when assessing alternatives’ performances

with the maximum number of evaluation factors in each region not exceeding four

(Cowan 2010). Figure 3.1 demonstrates the decision regions and corresponding

decision rules of the model.

Figure 3.1: The structure of evaluation factors, notions, decision regions, and

decision rules for members and sets

The evaluation begins with the screening region, as the filtering phase of the decision

process with a non-compensatory decision rule. Thus, alternatives, which fail to

satisfy the factors of this region, will be either removed or considered for redefinition.

We postulate a genuine interest in the first three evaluation factors which we call

concrete factors. Therefore, the screening region excludes attributes that; 1) are not

relevant to the decision context (coherency with objective; 2) are not commensurable

in a consistent manner and with a reasonable amount of effort (operational); and 3)

are not clearly distinguishing among all alternatives to perform a comparison

(discriminative). By establishing a screening region, we ensure that concrete factors

III- A methodology for selection of attributes

are not ignored in compensation for other evaluation factors. Attributes that meet

the three evaluation factors of the screening region move into the choice region. The

choice region operates with a compensatory decision rule, therefore, a compromise

among evaluation factors in this decision region is desired. The choice region

evaluates the attributes based on the four criteria including 1) “understandable”

when it has a clear and unambiguous definition; 2) “certainty” when it yields a certain

measured value for the objectives; 3) “directness” when it directly measures the

primary objective of the decision problem; and 4) “representative” when it

represents the essential characteristics of the system. The third group of factors

evaluates “sets of attributes” based on the optimal decision rule. The optimal decision

rule can be regarded as the optimized outcome for a set of attributes that capture the

maximum key aspects of all objectives (completeness) with optimized size of the

attribute set (concise). In addition, the set should not contain a double-counting

attribute (non-redundancy), which can be expressed as the constraint of the optimal

region (Zamanifar and Hartmann 2021).

3.6 Methodology and the Developed Framework

This section presents the methodology toward developing the attribute selection

framework, the framework itself, and methods used for implementing the

framework. Table 3.2 demonstrates the adopted methods in the frame of the

prescriptive decision analysis. While the problem structuring phase was presented

in section 3.5, this section discusses methods and their applications of the remaining

tasks of our research design.

Disaster Recovery Planning of Transportation Networks; Problem structuring and decision attributes

Table 3.2: An overview of the adopted methods and tasks for developing the

framework

Purpose

Task

Method

Problem

structuring

Adopting evaluation factors

Content analysis

Defining decision regions and assigning

decision rules

Based on the property of factors and

alternatives

Preference

elicitation

Identifying the relative importance of

compensatory evaluation factors

Cardinal-ranked based weights

Problem solving

Combination and extension of

compensatory and non-compensatory

MADM techniques

- Multi-attribute value theory

- Elimination by aspect

Implementation

and solution

handling

Collecting data

- Systematic review

- Questionnaire

Implementing methodology

Workshop with decision-makers

Analyzing data

Proposed methodology

Analyzing results

- Performance observation and

feedback survey

- Retrospective comparison

- Typology of selected attributes

- Shannon information entropy

3.6.1 Preference Elicitation

Imprecise weight elicitation is based on ordinal and cardinal values that DMs

approximate regarding the relative importance of criteria. Ordinal information refers

to the rank of criteria based on their importance, while cardinal information

represents the relative range of intervals among assigned ranks. Ordinal methods

such as Rank Ordered Centroid (ROC), Rank Sum (RS), and Rank Reciprocal (RR) (for

a review, see, e.g., Roszkowska 2013) convert the rank of criteria to (surrogate)

numerical weights. Unlike the approaches based on semantic and numerical scales,

weight approximation methods assume that compelling DM to express their exact

perceived values is cognitively demanding and refrain from obtaining viable

preferences (Barron 1996; Alfares and Duffuaa 2008). For example, Barfod and

Leleur (2014) argue that DMs are more comfortable and confident with ranking the

III- A methodology for selection of attributes

attributes rather than communicating their preferences by verbal scales.

Roszkowska (2013) highlights that for a group of DM is easier to agree on rank-based

sorting of items than to assigning precise numerical values. However, the critique

also exists that preference elicitation following ordinal methods encounters

information loss since these methods do not inquire or make use of information

regarding the magnitude or intensity of preference among sorted items (Danielson

and Ekenberg 2016). Rank-based methods generally rely on the centroid of ordered

factors and do not require any further input from DMs on the preference difference

between ordered pairs of factors. Some studies also report the victimized weight for

lower-placed criteria due to large discrepancy between the highest and lower sorted

criteria, suggesting the need for methods that incorporate cardinal information into

the weight approximation process and generate “smoother” weight (Roberts and

Goodwin 2002; Huang et al. 2011; Belton and Stewart 2002)

Building upon the existing weight approximation approaches (Kárný 2013; Salo and

Hamalainen 2001; Barron and Barret 1996), we designed a rank-based tool to allow

experts to communicate their cardinal and ordinal preference related to the relative

importance of four compensatory evaluation factors. The reason that we customized

a weight approximation approach instead of pure ordinal methods was first to avoid

extreme weights that significantly marginalize the weight of lower factors (Belton

and Stewart 2002), second to prevent equalizing impact on upper factors (Kunsch

and Ishizaka 2019), and third to utilize the available cardinal information that ordinal

methods often do not take into account (Danielson and Ekenberg 2016).

We used the input of six MCDA experts to suggest trade-offs among the evaluation

factors that represent criteria of a good attribute. In order to recognize participants

as experts, we considered the fulfillment of three criteria consisting of research

engagement in the MCDA field, current involvement in the field through MCDA-

related publications in the last five years, and post-graduates holding academic

research assistant positions. Since the properties of attributes in the decision-making

context have been widely discussed in decision analysis and MCDA discipline, we

chose to acquire the input of academic experts within this field. Experts provided

ordinal information for evaluation factors by ordering them from the most important

Disaster Recovery Planning of Transportation Networks; Problem structuring and decision attributes

to the least important on a vertically 2D visualized slider. They then adjust the

distance among the sorted evaluation factors on the slider to express their cardinal

preference information. Therefore, while experts can communicate the ordinal

preference by ordering the factors, they can also regulate the intervals among each

pair of sorted factors expressing the pairwise preference intensity. No numerical

scale has been presented for experts on the slider and visuospatial scale was the

interface for regulating the distances. The mathematical model that interprets the

defined rank and intervals into numerical weights can be formally articulated by the

following:

The input value for an evaluation factor 𝑖 is 𝑑𝑖 ∧𝑑1=0 where 𝑑 is Euclidean distance

of factors assigned by experts to the Cartesian origin 𝑂 of the vertically visualized

slider. Each evaluation factor is presented to experts as an item on this slider, while

the first factors always remain at the origin 𝑂. The assigned location of each item

represents experts’ ordinal preferences. Since the most important factor is set as an

item in the highest point of the slider, it is then logical to assume 𝑑1

󰆷≥𝑑2

󰆷≥ 𝑑3

󰆷≥

⋯ 𝑑𝑛

󰆷 for ∀𝑖 ∈𝑛, 9≥ 𝑛≥2 where 𝑑𝑖

󰆷 is the revisited distance of factor 𝑖 to a new

origin that increases as do the preference of factors. This assumption allows for

converting the growth of the distance from the origin equal to the growth of

preference. Therefore, for 𝑛=4 evaluation factors of the choice region, we have 𝑑1≤

𝑑2≤ 𝑑3≤ 𝑑4 which represents 𝑑1≽𝑑2≽ 𝑑3≽ 𝑑4. Now following the equations

below, the relative importance of factors can be calculated:

𝑣𝑜= √∑(𝑑𝑖−𝑑)2

𝑛

𝑖

(𝑛−1)−𝑘 +𝑑𝑚𝑎𝑥 (1)

𝑑𝑖

󰆷=|(𝑑𝑖− 𝑣𝑜) | ∗ln|(𝑑𝑖− 𝑣𝑜) | ; ∀𝑖 (2)

𝑤𝑖=(𝑑𝑖

󰆷∑𝑑󰆷𝑖

𝑛

⁄)∗100, (𝑖=1,…𝑛) (3)

𝑤=𝑤1 𝛾(𝑚)4

𝑐+ 𝑤2𝛾(𝑚)5

𝑐+ 𝑤3𝛾(𝑚)6

𝑐+𝑤4 𝛾(𝑚)7

𝑐 , ∑𝑤𝑖=1

𝑛

1,𝑑∈ ℝ ,𝑤𝑖≠0 (4)

where 𝑑 is the mean value of all distances from origin 𝑂. 𝑣𝑜 is the virtual origin point

of the weight vector as a base for calculating the revised distance, 𝑑𝑖 is the initial

distance for each interval that experts assign, 𝑘 is the number of evaluation factor

III- A methodology for selection of attributes

with equal ordinal preference (if there is any), 𝑛 is the number of factors, 𝑑𝑖

󰆷 is the

revised distance of each interval value to the 𝑣𝑜, and 𝑤𝑖 is the calculated weight of 𝑖th

factor when ∑𝑤𝑖=1

𝑛

1. We incorporated the exponential effect in Eq. 2 to prevent

equalized weights while allowing the weight vector to count for both ordinal and

cardinal preference input of DMs. Haung et al. (2011) point out that the non-linear

distances between single dimension scores and ratios should produce smoother

trade-offs. In addition, we know of no study that suggests preference of individual

related to a sorted list of objects is distributed uniformly (see Robert and Goodwin

2002). With this approach, we could shift the weight vector toward a flatter shape

and, in the meantime, prevent significant discrepancy between the weight of the first

and last factors.

By using the input of experts regarding the order and interval among four

compensatory evaluation factors, the weight factor can be delivered in the format of

Eq. 4. Experts ranked the four evaluation factors as the following: 𝛾(𝑚)5

𝑐≽𝛾(𝑚)6

𝑐≽

𝛾(𝑚)4

𝑐≽ +𝛾(𝑚)7

𝑐. The cardinal preferences could not be stored due to a lack of

storage capacity for the input information. Assuming that the preference for all

factors is judgmentally independent, the preferential model of the four evaluation

factors of the choice region, including understandable, representative, direct, and

certain, ( 𝛾(𝑚)4

𝑐, 𝛾(𝑚)5

𝑐, 𝛾(𝑚)6

𝑐, 𝛾(𝑚)7

𝑐 ) can be shown as the weight vector 𝑤=

20.68 𝛾(𝑚)4

𝑐+ 36.56 𝛾(𝑚)5

𝑐+ 27.44 𝛾(𝑚)6

𝑐+15.32 𝛾(𝑚)7

𝑐.

3.6.2 Models of Transition and Aggregation

Both compensatory and non-compensatory approaches have their own application

and advantages; hence, a contrast between them is not meaningful. Nonetheless,

there are decision contexts in which employing either of compensatory or non-

compensatory decision rules alone cannot meet the characteristic of the modeled

problem. Non-compensatory aspect-based methods rely on a sequential elimination

approach based on sorted criteria that usually leads to a straightforward selection of

the most preferred alternative. Non-compensatory methods are widely used in

normative decision theory (see, e.g., Gigerenzer and Goldstein 1996) since they are

consistent with the concept of bounded rationality. However, aspect-based non-

Disaster Recovery Planning of Transportation Networks; Problem structuring and decision attributes

compensatory methods overlook the existence of some criteria and a part of the

available information in the decision context is often regarded as irrelevant

(Rothrock and Yin 2008). This is because most of the information collected on

alternatives will not play a role in the evaluation process (Munda 2005). Therefore,

they are limited in application to conditions when non-compensatory is the desired

rule of the entire decision context. Meanwhile, compensatory methods cannot be

applicable when some criteria are infinitely more important than others. With this

preferential model, compensatory methods could lead to an undesirable outcome as

the choice might fail to meet the minimum level of desirability in one or more criteria.

Consequently, compensatory methods might not be efficient when a part of the

decision context does not accept trade-offs among some of the criteria. Both

compensatory and non-compensatory methods, when they are used individually,

assume that the same decision rule holds for all criteria. Therefore, for some

problems, they are unrepresentative of the decision strategy they seek to represent.

For the benefit of our framework, we combined the application of compensatory and

non-compensatory methods and designed two decision regions for appraising

isolated attributes within a single decision system. Integrating compensatory and

non-compensatory decision rules maximizes the amount of incorporated

information and allows its specificity within the modeling procedure. The first

decision region performs in a perfectly non-compensatory fashion, while the second

decision environment allows for a compensatory interaction among the factors. The

first decision region is absolutely preferred to the second decision region which we

mathematically formulated as part of the transition between two regions.

For the non-compensatory region, we adopt the axioms presented with the

lexicographical choice concept (Tversky 1972) and formulated it to an aspect-based

screening condition as it is formalized in Eq. 1. For the choice region, we directly used

the well-known Multi-Attribute Value Theory (MAVT) (Keeney and Raiffa 1993) and

contextualized it to the local variables of our decision context shown in Eq. 2. In doing

so, the following mathematical expression represents the integration of

compensatory and non-compensatory decision rules. The condition expressed in Eq.

1 indicates that alternative A is preferred to B when two alternatives have equal

III- A methodology for selection of attributes

performance on a set of factors in a binary format while there exists at least one factor

that alternative B is not satisfying. This means, for an attribute to proceed to the

choice region, it needs to satisfy each of the three non-compensatory evaluation

factors. Accordingly, for the first three evaluation factors (coherent with objective,

operational, and discriminative: 𝛾 1𝑠, 𝛾2,𝑠 𝛾3 𝑠) of the screening region: Let Γ𝑠=

{𝛾1𝑠,…,𝛾𝑖𝑠}, ∀𝑖∈{1,…,ℎ}, ℎ≥2 be the finite set of already known Concrete factors of

our screening region(𝑠) which is denoted by s. Now, suppose there exist a nonempty

finite set called 𝜗 that 𝜗 𝛾𝑖𝑠 represents the importance degree among factor 𝛾𝑖𝑠 where

𝑉 represents the preference of DMs on a factor and 𝑉 𝛾1𝑠=𝑉 𝛾2𝑠= 𝑉 𝛾3.𝑠. Moreover, let

Δ1={𝛿1𝑠,…,𝛿𝑗𝑠},∀𝑗∈{1,…,𝑚},𝑚>2 and a positive integer define the set of

competing alternatives and Ψ𝑖𝑗 denotes the binary value of 𝑖𝑡ℎ factor to 𝑗𝑡ℎ

alternative where Ψ𝑖𝑗 ∈{1,0}. Now consider 𝛿𝑗𝑠 and 𝛿𝑗+𝑛

𝑠∈ ∆,∀𝑛>0 then 𝛿𝑗𝑠 is

lexicographically preferred to 𝛿𝑗−𝑛

𝑠 if, and only if:

{

Ψ𝑖𝑗

𝛿𝑗𝑠 equals 1 for all Γ ={𝛾1𝑠,…,𝛾𝑖𝑠}

and,

∃𝛾𝑖𝑠 ∈ Γ that Ψ𝑖𝑗

𝛿𝑗−𝑛

𝑠 equals 0.

(5)

Meanwhile, for the choice region with compensatory decision rule, we aggregate four

evaluation factors of understandable, representative, direct, and certain ( 𝛾(𝑚)4

𝑐, 𝛾(𝑚)5

𝑐,

𝛾(𝑚)6

𝑐, 𝛾(𝑚)7

𝑐 ) with formulating MAVT for our problem. The transition from the

screening region to the choice region can be shown: again, let Γ󰆷𝑐=

{𝛾1𝑐,…,𝛾𝑖𝑐},∀𝑖:{1,…,𝑘},𝑘≥2 an integer for the new discrete finite set of Choice

factors of the choice utility region (𝑐) which is denoted by c such that Γ󰆷𝑐

󰆷∩Γ={∅}

󰆷,

∧ Γ󰆷𝑐

󰆷≻Γ𝑠

󰆷. Moreover, accept Δ󰆷2={𝛿1𝑠,…,𝛿𝑗𝑠},∀𝑗∈{1,…,𝑚} , 𝑚>2 as the choice set

that already satisfied the set of Γ𝑠 in the screening region such that Δ󰆷1⊆ Δ2.

Additionally, assume preference weight among factors follow 0>𝑉 𝛾1𝑐>𝑉 𝛾2𝑐>⋯>

𝑉 𝛾𝑖𝑐, then, without loss of generality, the utility of each alternative is:

Disaster Recovery Planning of Transportation Networks; Problem structuring and decision attributes

𝑈𝑖(𝛿𝑗𝑐)=∑𝜔𝑖

𝑛

𝑖=1 .Ψ󰆷𝑖𝑗(𝛿𝑗𝑐), 𝑖=1,…,𝑛, (6)

Where 𝑈𝑖(𝛿𝑗𝑐) is the scaled utility function of alternatives, Ψ󰆷𝑖𝑗 denote the

performance of attribute 𝑖∈ Δ󰆷 on alternative 𝛿𝑗𝑐∈Γ󰆷 as a single attribute value

function, (𝛿𝑗𝑐) is the performance of alternative 𝑗 for attribute 𝑖 and 𝜔𝑖 is scaling

factor projecting the importance weight of attribute 𝑖, ∑𝜔𝑖

𝑛

𝑖=1 =1. For further

investigation on the axiomatic background of the Eq. 6, one can see the original work

of Keeney and Raiffa (1993).

3.6.3 The proposed Framework

We designed the framework based on the evaluation factors, their preferential model,

and the decision rules as well as the adopted transition and aggregation logic. It

consists of nine steps which acts as a decision aiding toolkit for selecting attributes

of DRPTN problems. Figure 3.2 provides a detailed flowchart and the process of

applying the proposed framework.

III- A methodology for selection of attributes

Figure 3.2: The consecutive algorithm of the framework for the selection process of an

attribute set

The implementation of the framework begins with identifying the primary objectives

of the original problem. The original problem refers to the problem for which the

framework intends to select attributes. Since the framework embeds a choice model,

the task in the second step is to develop a set of alternatives. The alternative pool is

a set of candidate attributes as the input of the model for the evaluation process.

Disaster Recovery Planning of Transportation Networks; Problem structuring and decision attributes

Regardless of the approach used in constructing such a set, it is essential to establish

an expanded and complete set of attributes from diverse sources such as literature,

experts, stakeholders, actors, and decision-makers to obtain a “reasonably complete”

list of attributes (Keeney 2007).

The third step is adopting the ten evaluation factors for the three evaluation stages

as well as the relative importance among the four evaluation factors of the choice

region. In step four, Eq. 5 indicates that alternatives for which the necessary condition

of all three screening factors is not held must be ruled out or redefined. Within the

fifth step, the remainders of alternatives enter the choice region in which users can

assign a numerical value for attributes’ performance in relation to satisfying

compensatory factors. Once each alternative has received the scores of the previous

step, in step six, an additive aggregation method (Eq. 6) is recommended to rank the

alternatives under the compensatory decision rule. During the evaluation, users can

redefine or suggest new attributes to satisfy the screening evaluation factors or

improve the performance on the choice evaluation factors, under the condition that

the evaluation process iterates from the second step.

Concept mapping of ranked attributes is the aim of the seventh step, by assigning

each ranked attribute from the previous step to its representing objectives. In

accordance with Keeney’s recommendation (Keeney 1992), we suggest the generic

value tree as the concept mapping approach to aid in identifying the completeness of

the attribute set. The last step inherits the ranked list of attributes from screening

and choice regions that are classified within the organization of the conceptual value

tree of the defined objectives. In this step, the task is to evaluate sets of attributes

based on completeness, size, and non-redundancy. Using the value tree, the

completeness of the set can be monitored with regards to covering all objectives. In

the optimal region, the minimum size of the attribute set that satisfies the

completeness of the set and does not contain a double-counting attribute is the

selected attribute set. If the resulting ranked attributes of step seven could not cover

all the objectives of the value tree, expanding the alternative pool is necessary.

III- A methodology for selection of attributes

3.6.4 Methods of Implementation

For obtaining a degree of validation and investigating the performance of the

framework, we conducted an experiment to test the implementation of the

framework in the context of mid-term disaster recovery planning of the Tehran

transportation network. We sought to select an attribute set for optimizing the

performance of the network recovery process after a major earthquake. In doing so,

we collected data from literature of DRPTN and disaster recovery experts to obtain a

list of candidate attributes as the input of the framework. A systematic literature

review of 46 papers allowed us to extract 34 attributes from DRPTN publications.

Additionally, we collected ten additional unique attributes from 23 decision-makers

of crisis management organizations in Tehran using a paper-administrated survey.

Thereafter, we organized a workshop and followed the steps of the developed

framework that is presented in section 3.6.3. We acquired the input of a focus group

that includes four senior members of a group of city planners and emergency

managers who had previously developed the disaster recovery planning of the

Tehran transportation network. Before the evaluation session, we explained the

structure and function of the framework and discussed the problem by presenting a

brief disaster scenario as well as detailed descriptions and definitions of the

evaluation factors. For the sake of consistency with a real-life instance of the DRPTN,

we accepted the previously defined objectives for the same problem that the focus

group had formulated. The objectives were maximizing accessibility and mobility as

the properties of the network, and maximizing recovery effectivity and recovery

efficiency as the properties of the recovery process.

At first, DMs evaluated the alternatives based on the three non-compensatory

evaluation factors of the screening region and assigned a binary value of 1 or 0.

Following the non-compensatory decision rule shown in Eq. 5, alternatives were

screened and transmitted to the choice region. In the next step, DMs used a direct

rating on a local scale of 0 to 10. The group was also free to redefine the attributes

that have not satisfied the evaluation factors of the screening region. DMs deliberated

on the score of each attribute and communicated it verbally once a consensus was

reached. This process varied for different attributes. Sometimes disagreements

Disaster Recovery Planning of Transportation Networks; Problem structuring and decision attributes

required more extended discussion to be resolved, particularly in the presence of an

opposite voice, and in other cases, the value assignment process was relatively fast.

In the screening region, three attributes have been excluded using a majority vote

where no consensus could be reached. We observed that conflicts mainly occurred in

the screening and optimal region, while the evaluation process in the choice region

encountered some relatively minor disagreements resulting in less controversial

discussion. In both screening and choice regions, critical issues were resolved by

allowing experts to redefine or improve attributes that failed to meet non-

compensatory evaluation factors. As subject-matter experts, participants had prior

experience analyzing possible attributes for disaster recovery planning of Tehran

transportation network and emergency network planning. Once the scores had been

documented, we used the weight vector presented in 3.6.1 and Eq. 6 to aggregate DMs

inputs and solve a utility choice problem that resulted in a ranked list of attributes.

Consequently, we used a conceptual value tree of objectives to assist DMs in assigning

each ranked attribute to the representative objectives. In the last step, DMs selected

a set among ranked attributes which satisfied the optimal region's three factors and

constituted the recommended set. The evaluation session took 3:07 minutes, while

the total time of the subject-relevant discussion was 2:42 minutes.

Finally, to analyze the performance of the framework and the resulting attributes of

the case study, we began by investigating the typology of the selected attributes

according to Keeney’s recommendations (Keeney 1992). Keeney characterized

attributes as three different types: Natural, Proxy, and Constructed. Natural

attributes directly measure the degree to which an objective is met and can be

counted or physically measured. Proxy attributes share features of natural attributes

but are less informative and do not directly indicate the achievement of an objective.

Constructive attributes are developed when there are no natural attributes for the

objective of the concern. The certainty and accuracy of these attributes might be less

than Natural attributes with respect to measuring the objective, but their presence is

essential in the absence of natural attributes (Keeney 2007). Secondly, we

determined the source of inclusion of attributes in different stages of the evaluation

process and in the ranked list of attributes to understand how the population of the

III- A methodology for selection of attributes

attributes in each stage is distributed. Thirdly, we compared the resulting attributes

of the framework to the list of working attributes previously selected by the

participating experts for the same planning in the case area. Fourthly, we used the

Shannon information entropy approach (Shannon 1948) to understand the

distribution of information and its specificity in the choice region among

compensatory decision factors. Shannon entropy information analysis has been used

for sensitivity analysis, analysis of information distribution in criteria system, or

assigning quasi-objective weights to criteria in MADM (e.g., Qi and Guo 2014; Wu et

al. 2011; Liu and Chen 2018). This analysis was initially introduced within the

information theory context to estimate the degree of disorder and randomness in the

original data using probability theory (Penjani Hopkins and Erden 2020). Entropy, in

information sensitivity context, is an index representing the discrimination ability of

the information that is assigned to the value of alternatives for a certain criterion,

assuming that the diversity of assigned information to alternatives based on a

criterion has a linear association with the specificity of that criterion. Entropy

information analysis follows a set of straightforward calculations based on a decision

matrix 𝑅 in which alternatives are scored against criteria. Assume there is a set of 𝑚

alternatives and a set of criteria with 𝑛 member in a decision matrix, where

𝑥𝑚𝑛 represents the performance of 𝑖𝑡ℎ alternatives on 𝑗𝑡ℎ criterion ( 𝑖=

1,2,...,𝑚; 𝑗= 1,2,...,𝑛) as below:

𝑅=[𝑥11 𝑥12 … 𝑥1𝑛

𝑥21 𝑥22 … 𝑥2𝑛

⋯ … ⋱ ⋮

𝑥𝑚1 𝑥𝑚2 … 𝑥𝑚𝑛]

The entropy value and relative weights of criteria can be calculated following a series

of steps (Penjani Hopkins and Erden 2020; Hwang and Yoon 1981). First, the raw

data of performance indices in the decision matrix is normalized using Eq. 8 to bring

all values in an identical dimension in case they are inputted under different scales

and units. 𝑝𝑖𝑗 = 𝑥𝑖𝑗∑𝑥𝑖𝑗

𝑚

𝑖=1

⁄; ∀𝑖,𝑗

(8)

(7)

Disaster Recovery Planning of Transportation Networks; Problem structuring and decision attributes

Once the normalized matrix is obtained, we arrive at 𝑝𝑖𝑗 as the standardized value of

a non-negative non-zero index. Afterward, the entropy value (𝐸𝑗) can be computed

following the Eq. 9, where 𝐾=(ln 𝑚)−1 is a constant to hold the value of 𝐸𝑗 between

0 and 1. Meanwhile, (𝑝𝑖𝑗ln𝑝𝑖𝑗) is agreed to get the value of zero if 𝑝𝑖𝑗=0 (Lotfi and

Fallahnejad 2010).

𝐸𝑗=−𝑘 ∑𝑝𝑖𝑗ln𝑝𝑖𝑗 ;∀𝑗

𝑚

𝑖=1

Now, ( 1−𝐸𝑗) represents the diversification value for each criterion ( 𝐷𝑗). It

determines how a set of information content assigned to alternatives is divers based

on 𝑗𝑡ℎ criterion (e.g., performance score, retrospective data, observed

measurements, expected value, or similar). The lesser the value of 𝐸𝑗, the greater the

degree of differentiation of values assigned to alternatives, which suggests that more

information can be derived from the criterion. Similarly, a larger value of 𝐷𝑗, is due to

the larger variation of values in the 𝑗𝑡ℎ criterion’s, which is assumed to be associated

with information specificity within a criterion. It means the less diversification, the

more entropy, and therefore the less information (Penjani Hopkins and Erden 2020).

Finally, Eq.10 gives the entropy-based importance for each criterion that determines

the information value of criteria based on their entropy:

𝑤𝑗= (1−𝐸𝑗)

∑(1−𝐸𝑗)

𝑛

𝑗=1 ; ∀𝑗

The last analysis on the performance of the framework was issued to obtain the focus

group’s feedback to two questions: 1) as users, to what degree are you satisfied with

the application of the framework, and 2) to what degree do you agree with the

improved quality of the framework’s outcome compared to the previously selected

attributes. We used an anonymously printed-format survey based on a 5-point Likert

scale (Joshi et al. 2015) two days after the workshop. Additionally, we performed an

unstructured group discussion with open-end questions that lasted approximately

30 minutes immediately after the workshop, allowing DMs to openly communicate

the experience of using the framework.

(10)

(9)

III- A methodology for selection of attributes

3.7 Result and Synthase

3.7.1 Performance of the Framework in the Implementation Process

We followed the steps of the framework and applied it to the Tehran DRPTN problem.

Having 57 candidate attributes as the input of the framework, the screening region

filtered 42% of alternatives that failed to meet at least one of the non-compensatory

evaluation factors. Therefore, the compensatory evaluation in the choice region

began with 33 attributes that formed 58% of the initial alternative pool. Table 3.3

highlights the number of alternatives in each stage of the evaluation process.

Table 3.3: Number and share of attributes in decision regions of the evaluation process

Number

Examples

Proceed into the screening

region

100%

Full list available at:

https://doi.org/10.14279/depositonce-10019

Filtered in the screening

region

42.1%

Lifeline interaction, traveler convince, link

geometry, damage complexity

Proceed into the choice

region

58%

Depot and need points, traffic redundancy, centrality

measures, redundancy

Proceed into the optimal

region

26%

Link topology, capacity, social vulnerability* link

delay, recovery efficiency

The outcome of the choice region yielded a ranked list of attributes that was

preliminary to organizing a generic value tree based on the primary objectives. In the

optimal region, the distribution of eight first ranked attributes to the objectives was

required the way that all objectives receive at least one representative attribute.

Similarly, DMs assigned the first 11 attributes to the value tree to provide each

objective with no less than two attributes. To be able to provide three available

choices for all four objectives, assigning 16 first-ranked attributes was required. That

supports the transmission of 16 attributes to the optimal region (approx. 26% of the

alternative pool). Table 3.4 shows the first 16 attributes assign to four objectives until

each objective receives at least three attributes.

Disaster Recovery Planning of Transportation Networks; Problem structuring and decision attributes

Table 3.4: The generic distribution of the first 16 attributes to the respective primary

objectives

Objective

Rank 1

Rank 2

Ranke 3

Rank 4

Ranke 5

Maximize

recovery

effectivity

Travel delay of link

* link flow

Impact on Total

Network Travel

Time

Social

vulnerability*

link flow

Social

vulnerability*

zone travel

demand

Maximize

recovery

efficiency

Travel time

improvement per

resources

Travel time

improvement/

recovery duration

Recovery

efficiency

Maximize

accessibility

Access level to the

service providing

nodes

Centrality

measures

East-west and

north-south

connectivity

Connectivity to

other traffic

zones

Network

topology

Maximize

mobility

Link capacity

Annual Average

Weekly Traffic

Annual Average

Daily Traffic

Traffic density

Based on the arrangement of the rank attributes on the value tree, the DMs selected

six attributes as the recommended set of decision attributes for the DRPTN problem.

The set contains the first five ranked attributes as 1) access level to Service Providing

(SP) nodes; 2) product of link travel delay and traffic flow; 3) travel time improvement

per recovery duration; 4) travel time improvement per resources; and 5) centrality

measures plus Link capacity that is ranked as the eighth attribute. The recommended

set covers the main concerns of the decision problem based on the primary objectives

and is supposed to be complete and non-redundant with optimized size. Table 3.5

provides a brief description of the selected attributes.

III- A methodology for selection of attributes

100

Table 3.5: A brief description of attributes of the selected set

Selected attributes

Brief description

Access to service

providing places

The topographical capability of links in providing access to the location of critical

facilities and service providing nodes on the network.

Link capacity

The ability of each link to carry the traffic as a measure of mobility performance of

a link.

Travel time

improvement (TTI)

per resources

The amount of machinery or monetary resources that have to be assigned to achieve

a certain improvement in travel time on the network.

Travel time

improvement per

recovery duration

The amount of consumed unit of time to achieve a defined travel time improvement

in the network

Travel delay * link

flow

The travel delay time that closure of a link imposes to a specific O-D trip integrated

to the amount of the traffic volume that the link sustains.

Centrality measure

Topological importance of a link in a network graph regardless of the traffic flow.

Table 3.6 demonstrates the properties of each selected attribute of the recommended

set and their representing objectives. The calculated utility based on the

compensatory factors as well as the rank of each attribute irrespectively indicates the

score and ordinal importance of attributes. The selected set consists of four natural

attributes, one constructive, and one proxy attribute. The range of the assigned utility

of attributes was between 14.22 to 29.67 while the best utility could ideally be 30.3,

and 3.03 for the worst utility.

Table 3.6: Rank, calculated utility, representing objectives, and type of attributes of

the selected set

Attribute

Access level to

critical nodes

Travel delay of

link * link flow

TTI/resources

TTI/recovery

duration

Link centrality

index

Link

capacity

Rank

(1)

(2)

(3)

(4)

(5)

(8)

Utility

29.675

29.375

28.912

28.448

27.942

25.878

Type

Natural

Constructive

Natural

Proxy

Natural

Objective

Accessibility

Effectivity

Efficiency

Accessibility

Mobility

Disaster Recovery Planning of Transportation Networks; Problem structuring and decision attributes

101

3.7.2 Synthesis of the Framework’s Outcome and Feedback of

Participating DMs

Table 3.7 shows that the literature of DRPTN contributes to 59.64% of the initial

alternative pool while the survey with experts formed 17.54% of attributes.

Additionally, 13 attributes (22.8%) were added to the alternative pool during the

evaluation process as by-products of the framework. Similar to the initial population

of the alternative pool, in the first 10 and 20 ranked attributes, literature-based

attributes have the largest share. In the selected set, half of the attributes belong to

the literature review’s output while the rest were introduced during the workshop.

Results show that while collected attributes from 23 disaster managers DMs occupy

22.8% of the population of the initial alternative pool, they contribute the least in all

ranked attribute classes and have no representative within the selected set.

Table 3.7: Distribution of attribute based on their source in the initial pool, first 5, 10,

and 20 ranked attributes

Selected

set

The first 5

ranked

attributes

The first 10

ranked

attributes

The first 20

ranked

attributes

33 attributes of

the choice

region

The initial

alternative

pool

Redefined

50%

60%

30%

30.3%

22.8%

Experts

Survey

30%

20%

21.2%

17.5%

Literature

50%

40%

50%

48.5%

59.6%

Table 3.8 shows the retrospective attributes which had been selected by participating

DMs, for the same problem and the same geographical context as the working

attributes of Tehran DRPTN. Model-driven attributes refer to the attributes selected

by DMs following the proposed framework of the current paper. Two sets share two

identical attributes based on equal serving objectives. The size of the model-driven

attribute set is six members while the working attribute set contains nine attributes.

III- A methodology for selection of attributes

102

Table 3.8: An overview of the selected attributes by the framework and previously

selected attributes by the DMs in an unaided process

Objectives

Accessibility

Effectivity

Efficiency

Mobility

Size

Model-

driven

Attribute

Access level to critical

nodes, Link centrality

index

Travel delay of link

* link flow

TTI/resources,

TTI/recovery

duration

Link

capacity

Working

attributes

Access level to critical

nodes, access to main

highways, west-east-

north-south connectivity

Proximity

population, Peak

hour traffic flow

Traffic flow

improvement/re

source, Recovery

duration

Link

capacity,

Density

Table 3.9 shows the result of the information entropy analysis of the compensatory

evaluation factors in the choice region. As described in subsection 3.6.4, the entropy

values represent an index suggesting the amount of the information stored in each

evaluation factor based on the DMs’ input values during the evaluation process.

Accordingly, 𝐸𝑗 indicates to what extent information is preserved in an evaluation

factor. Diversification value (𝐷𝑗) suggests the extent of the domain of input values

that DMs assigned to the alternatives. Based on the entropy analysis, the contribution

of information in the final ranking is determined according to the sensitivity of DMs

to the performance score of alternatives on evaluation factors. Therefore, the

calculated 𝐸𝑗 and 𝐷𝑗 are directly influenced by relative comparison on the scores

assigned by DMs. Following steps described in 3.6.4, related computation and values

of 𝐸𝑗 and 𝐷𝑗 are depicted in Table 3.9. Consequently, “certainty” and

“understandability” factors have less entropy value while diversification value is the

least for “directness” and “representative”. It means the value assigned by DMs varied

more when scores for the alternatives were based on “understandability” and

“certainty”, therefore, more information concerning these two factors is added in the

decision process. Conversely, the performance scores assigned by DMs were less

different (more even) evaluating attributes based on “directness” and

“representative” factors.

Disaster Recovery Planning of Transportation Networks; Problem structuring and decision attributes

103

Table 3.9: Results of the information entropy analysis of evaluation factors of the

choice region

Understandability

Directness

Representative

Certainty

−∑𝑝𝑖𝑗ln𝑝𝑖𝑗

𝑚

𝑖=1

-3.40946

-3.46100

-3.43188

-3.40333

Entropy (𝐸𝑗)

0.97510

0.98984

0.98151

0.97335

Diversification (𝐷𝑗)

0.02489

0.01015

0.01848

0.02664

Scaled to sum 1

0.31050

0.12662

0.230

0.3323

With respect to the users of the framework, the results of the survey communicate a

“moderately to strongly satisfactory” application of the framework while the majority

of DMs were “strongly agree” with the quality of the framework’s outcome as the

selected attribute set of the DRPTN problem. Table 3.10 shows the response of the

participants to the question addressing to what degree users were satisfied with the

application of the framework and Table 3.11 is the response to the question that to

what degree do they agree with the improved quality of the framework’s outcome

compared to the previously selected attributes.

Table 3.10: Agreement degrees to the quality of the selected

Strongly

agree

Moderately

agree

Neutral

Moderately

disagree

Strongly

disagree

DM1

DM2

DM3

DM4

Table 3.11: Satisfaction degree for using the framework set

Strongly

satisfied

Moderately

satisfied

Neutral

Moderately

dissatisfied

Strongly

dissatisfied

DM1

DM2

DM3

DM4

III- A methodology for selection of attributes

104

During the open discussion after the workshop, DMs confirmed that it was not

foreseen for them to select an attribute set that significantly differed from the one

they had previously selected. All participants agreed that disciplined and structured

evaluating of candidate attributes could lead them to revisit the current working set

of attributes. Two DMs were not completely satisfied with the evaluation process in

the choice region due to the number of alternatives. One DM expressed that the

evaluation process in the choice region was not as easy as it was for the screening

region with non-compensatory decision rules. Another DM took a similar stance and

suggested a mechanism to reduce the size of the alternative set in the choice region,

while two other participants found the evaluation process of the framework

relatively easy to use. Finally, DMs responded positively to whether the resulting

attribute set fairly reflects a complete range of their interests and values concerning

the objectives of the planning.

3.8 Discussion

Based on the characteristics of the framework and analysis of its outcome, the

following argument discusses the reasons why we believe the application of the

framework was successful. First, since the screening region allows for pre-evaluation,

the framework is inclusive and open to alternatives suggested by diverse sources

such as experts’ opinions and literature. The framework also accepts the redefined

attributes during the evaluation process which not only increases the likelihood of

reaching a complete set of attributes, but also provides a basis for brainstorming,

critical thinking, and creative input into the model. Harnessing the benefit of

integration of compensatory and non-compensatory techniques, alternatives are

evaluated in a thorough yet manageable manner. Therefore, although the modeled

process is flexible in accepting alternatives as inputs, it is rigorous in evaluating them

since only 26% of attributes from the alternative pool proceeded into the optimal

region and above 42% of attributes were filtered in the screening region.

Additionally, 100% of alternatives were evaluated at least once, while at least two

stages of evaluation took place for 52% of alternatives, and 26% of alternatives have

been assessed three times. Filtering 42% of attributes in the screening region could

Disaster Recovery Planning of Transportation Networks; Problem structuring and decision attributes

105

suggest a rigorous screening process due to the number of attributes in the

alternative pool. Pre-evaluation or size of the alternative pool could impact this

process, while the trade-off between the completeness of the input attribute list and

rigor of the process should be taken into account.

Secondly, the framework remains contextual and problem-dependent because the

evaluation process relies on the primary objectives of the original problem as the

benchmark for the selection of candidate attributes (steps 1 and 2), evaluation (steps

4 and 5), and identifying the generic class of attributes for the final selection (steps 7

and 8). Furthermore, the dependency of the framework on the decision context

resulted in the presence of four natural attributes in the selected set, which suggests

the directness of the attribute set and context-centric performance of the framework.

Moreover, the model not only evaluates individual attributes but also appraises the

properties of desirable sets of attributes of the targeted problem, ensuring the non-

redundancy and completeness of the set based on the primary objectives. Thirdly, the

framework does not impose a significant cognitive burden because the evaluation

factors are divided into three independent regions with a maximum size of four

factors in a flat hierarchy format. It allows that individual judgments, in both

articulating preferences among four compensatory evaluation factors and value

assessments, remain in a relatively reasonable state (Bond et al. 2008; Marttunen et

al. 2017; Cowan 2010).

Furthermore, evident from the experiment and participants’ feedback, the

structured, step-by-step framework of the model promotes an amount of supervision

over the inevitable subjectivity associated with the attribute selection by allowing to

track and locate where subjectivity might influence the evaluation process. Hence,

the selected attributes are less likely to be prone to bias and error than attributes

selected without a systematic, tractable, and transparent procedure. Based on the

post-workshop survey, the model-driven attributes meaningfully integrated the

concerns, values, and interests of the DMs into the decision analysis with a reduced

size of the set compared to the previously selected attributes. However, we cannot

dismiss the possibility that the positive feedback of the DMs could have originated

from availability heuristic, courtesy, etc., and future research must re-implement this

III- A methodology for selection of attributes

106

methodology in different settings.

The share of the redefined attributes during the workshop in the selected set, first

10, and 20 list of attributes suggests that the framework is likely to promote creative

and critical thinking. Additionally, we observed that the evaluation factors and the

evaluation process framed the discussion and provided a ground for brainstorming

and collaborative decision-making. Moreover, according to Table 3.7, while the

academic literature provided 50% of attributes of the selected set, DMs’ local

knowledge contributes to the other half of the attribute set which indicates the

performance of the framework with regard to balance incorporation of available

knowledge sources.

Results of the information entropy analysis suggest that DMs were more sensitive to

the performance of attributes based on “certainty” and “understandability” factors,

since the assigned values were more diverse for those factors and uniform for

“directness” and “representatives” factors. This arrangement of information entropy

is because first, attributes of the alterative pool originated from relevant literature

and experts that are likely to be sufficiently representative and direct. Second, the

non-representative attributes were already excluded thanks to the screening region

and the condition of “coherency with primary objectives.” Assuming that DMs fully

understand the definition of evaluation factors, the result of entropy analysis could

suggest that “certainty” and “understandability” of an attribute have higher relative

importance for the DMs who used this framework in the workshop. Therefore, for the

DMs of the case study, a certain and non-ambiguous disaster recovery planning,

although not necessarily optimal, is preferred.

The developed framework can offer a practical application in the disaster resilient

infrastructure context as it can support the problem structuring of these problems by

facilitating the identification of problem-relevant decision attributes. The same

process can (supposedly) be applied to other similar contexts, since selecting

decision attributes is the primary and critical step of decision analysis and modeling

in general, particularly when the popularity of MCDA in environmental, engineering,

and management studies is growing (Keisler and Linkov 2014; Bruen 2021).

Employing a systematically selected set of attributes for decision models could

Disaster Recovery Planning of Transportation Networks; Problem structuring and decision attributes

107

reduce the uncertainty related to decision factors in multi-objective or multi-criteria

decision-making models. This study suggests that in the problem structuring phase

of decision modeling, analysts employ the suggested framework or any other

systematic attribute selection process to increase the likelihood of achieving a viable

attribute set.

3.9 Limitations

Different preference elicitation techniques deliver different weights and the same

holds for different experts. While weighting vectors mainly depend on the method

and experts that generate them, uncertainty regarding the used preference elicitation

method in this study still stands. Using any preference elicitation method due to the

absence of a known solution or “true weight” cannot claim superiority. More evidence

from the application of the employed method in section 3.6.1 is needed to provide a

level of confidence in the trustworthiness of the generated weights. The preference

elicitation process could be subjected to re-implementation, uncertainty analysis, or

a wider domain of analysis to increase confidence in the robustness of weights.

Having said that, future users of the framework could use other approaches to supply

the relative importance coefficients of compensatory evaluation factors.

In this study, two major types of uncertainty are identifiable within the process. First

is the uncertainty related to the application of the attributes in terms of measuring

DRPTN objectives, and second is the uncertainty of the selection process. Uncertainty

within the selection process can be related to the individual subjective value

assignment, group dynamics, and preference determination. Uncertainty of

attributes application is due to the lack of experimental investigation on the quality

of attributes. Further evidence is required from 1) the application of this framework

in different settings and 2) the application of the produced attributes in real-life

problem or modeled disaster scenarios. For the former, we invite studies to employ

the proposed framework, while the latter, we aim to address it in future research.

III- A methodology for selection of attributes

108

3.10 Conclusion

While social and infrastructure systems encounter an unprecedented risk of climate

change and natural hazards, it is of paramount significance to develop DSSs that pave

the way for well-informed collaborative decision-making. To develop such a DSS,

modelers should feed the decision models with equitable and plausible attributes

that are the result of a tenable systematic selection framework. This study sought to

bridge the identified knowledge gap in the problem structuring of multi-criteria

decision problems by proposing a choice-screening model to assist in the evaluation

of decision attributes and prescribe a set. We illustrated the developed framework

with a case study to select decision attributes of a disaster recovery planning

problem. The innovative integration of compensatory and non-compensatory

aggregation methods within a newly designed sequential, 3-stage evaluation process

constituted the developed framework. The formalized attribute selection process

facilitated harnessing DMs’ knowledge and consequently led to a set of attributes of

the case problem, although further evidence from field experiments or simulated

implementation is required to support the quality of the produced attributes. DMs

were able to systematically evaluate attributes and collaboratively produce a ranked

list of attributes as well as the final selected set. We investigated the performance of

the framework based on the typology of the produced results, the discussed

characteristics of the framework, and the feedback from users. Observing the

development of the discussion in the workshop and position of the redefined

attributes in the final rank, it is not implausible to conclude that the evaluation

mechanism within the framework facilitates critical and creative brainstorming, thus

fostering the incorporation of the available knowledge sources. Using the proposed

framework, one must take into account the size and completeness of the alternative

set. A so-called diverse complete set of alternatives is required since the result will

be as complete as the alternative pool. Nevertheless, analysts and further users of the

framework must establish a balance between the desired completeness and the

complexity of the model. One should also note that the effectiveness of the selected

Disaster Recovery Planning of Transportation Networks; Problem structuring and decision attributes

109

set remains dependent on recognition of the right problem and consequently

defining the right objectives, since the framework remains true to the defined

primary objectives of the decision problem.

This question of the extent to which decision aid interventions are successful in

controlling the subjectivity and guiding the intuitive feelings to rational judgments

has been discussed widely in other disciplines. However, data-driven, systematic, or

evidence-based approaches do not always make a decision-making process immune

to epistemological errors (Power et al. 2019). Therefore, we cannot rule out a

possible implication of common cognitive biases prevalent in many decision

processes. Nevertheless, it is reasonable to assume that the systematic attribute

selection process could allow analysts to track and locate where subjectivity might

influence the evaluation process. For further use of this framework, we suggest that

a moderator oversees the evaluation session and acts as an opposite voice, if

necessary, to facilitate the extraction of DMs’ knowledge. Research and practice can

both use the proposed framework for establishing an equitable set of attributes of

decision problems, and even one who is not necessarily an expert in decision analysis.

Future research must employ a systematic approach towards the identification and

selection of decision attributes. Research must also dedicate more time and effort to

a solid problem-structuring phase before formulating a decision problem, specifically

with regard to complex and critical problems, such as those which address

environmental challenges and disaster resilient infrastructure planning.

III- A methodology for selection of attributes

110

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Chapter IV

DECISION ATTRIBUTES

OF DRPTN

“Decision aiding is meant to assist in constructing, establishing, and arguing for convictions.”

Bernard Roy (1996)

IV- Decision attributes of DRPTN

118

4 Decision Attributes of DRPTN

(Pre-print)

Zamanifar M, Hartmann T, (2021), Decision attribute for disaster

recovery planning of transportation networks; A case study.

Another version of this paper is published at the Journal of Transport Research Part D:

Transport and Environment by Elsevier with the following Digital Object Identifier (DOI):

https://doi.org/10.1016/j.trd.2021.102771

4.1 Summary

This paper implements a structured framework to suggest decision attributes of

transportation network disaster recovery planning. For this purpose, we collected 57

decision attributes from the relevant literature and experts’ opinions. Following a

framework with three sequential evaluation stages, decision-makers systematically

assessed the attributes based on each evaluation stage’s specific criteria. Thereafter,

we aggregated the decision-makers’ input values using a combination of

compensatory and non-compensatory Multi-Attribute Decision-Making techniques.

Results offer a ranked list of attributes and a recommended set of attributes for

Tehran’s road network as our case study. The findings suggest six attributes to be

included in road network disaster recovery planning as 1) access level to service-

providing nodes, 2) integration of link travel delay and traffic flow, 3) travel time

improvement per recovery duration, 4) travel time improvement per resources, 5)

Contributions: The idea was built upon the advice of the second author, and he also proofread and

commented on the general structure and communication of the paper. Both authors collaborated in the

revision of the paper. The first author performed the focus group workshop, post-workshop analysis,

interviews, literature search and survey, data analysis, drafting the paper, and establishing the

discussion.

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centrality measures, and 6) link capacity. However, the recommended attributes are

valid only when they remain as a set. Results contribute to the existing knowledge

about concerns and values in the reconstruction and recovery of transportation

networks after disasters. Transportation network planners and disaster managers

can use the recommended attributes as key factors for post-disaster decision support

systems or for evaluating available disaster resilience plans. Additionally, future

research can adopt this research outcome as an input for the problem structuring

phase of disaster recovery models.

4.2 Introduction

In the aftermath of a disaster, every decision’s reliability is vital due to its potential

impact on human life and socio-economic loss or gain. To support such decisions,

studies developed decision models for Disaster Recovery Planning of Transportation

Networks (DRPTN) that prioritize reconstruction operations on the network’s

components. Decision Support Systems (DSS) have been broadly used in the field of

DRPTN to recommend decisions for an optimized reconstruction sequence of

transportation links (for a review, see, e.g., Goujon and Labreuche 2015). Multi-

objective and multi-attribute decision-making models have been serving DSSs that

commonly yield optimum or compromise solutions (see, e.g., Galindo and Batta 2013;

Colorni et al. 2019). While the extent of our knowledge on the validity of such models

is limited, it is more or less accepted that the quality of outcomes depends on the

model’s decision parameters (Keeney 1992). One strand of decision parameters is

attributes that measure the achievement of objectives of a decision problem. Even for

decision models that are formulated with novel techniques and solved with

sophisticated, intelligent algorithms; the merit of the decision remains dependent on

“the completeness of the model in representing the real system” (Taha 2007), which is

conditioned to the presence of well-thought-out decision attributes (Kenney and

Gregory 2005). Notably, in the complex problem of DRPTN, the representativeness

and completeness of a model are challenging yet critical and depend on the adopted

attributes (Winter et al. 2018; Comes 2016). Therefore, the degree to which the

uncertainty associated with identifying attributes is controlled contributes to the

IV- Decision attributes of DRPTN

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certainty and reliability of recommendations the model prescribes (Gregory and

Failing 2002; Beven et al. 2015). This demonstrates the importance of defining

tenable attribute sets for a DRPTN problem.

DRPTN studies have introduced a broad range of attributes to optimize or rank post-

disaster recovery operations of transportation networks. However, insufficient work

has been done to establish a sound argument as to how the problem of DRPTN is

structured or key attributes are identified (Zamanifar and Hartmann 2020). Defining

attributes for the problem of disaster recovery can be inherently error and bias-

prone due to the non-observability of the post-event prescriptive model of the

DRPTN problem and inevitable subjectivity associated with problem structuring in

general (Cochran et al. 2011). Challenges arise during the selection of attributes since

epistemic and aleatoric errors can propagate into the decision model’s output even if

the model is mathematically solvable and verifiable (Phillips-Wren et al. 2019;

Wesley and Dau 2017; Beven et al. 2015). Furthermore, some reviews highlighted the

absence of systematically produced attribute sets for disaster management models

and pointed out the shortcomings (e.g., Zamanifar and Hartmann 2020; Gutjahr and

Nolz 2016), which indicate the emerging necessity of a model-driven set of DRPTN

attributes with supervised subjectivity. On this ground, the present paper suggests a

set of attributes of a DRPTN problem that is the product of a systematic multi-stage

evaluation and selection process. We developed a prescriptive decision model based

on three decision regions with compensatory, non-compensatory, and optimal

decision rules. First, we extracted data from the DRPTN literature as well as disaster

management experts’ input to identify the alternative pool containing candidate

attributes of DRPTN problems. Second, we adopted ten evaluation factors as the

criteria based on what the MCDM literature has suggested that represent desired

properties of a good attribute and a good set of attributes. Consequently, we

identified the trade-off among the factors that function under the compensatory rule.

After that, a group of transportation network disaster recovery planning experts,

who previously developed the DRPTN plan of the case study, systematically and

critically evaluated attributes against those evaluation factors through three decision

regions (for research data see Zamanifar 2020). Results suggest a ranked list and the

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selected set of attributes tailored for the DRPTN problem case of Tehran (Iran) in the

mid to long-term recovery phase that satisfies evaluation factors and addresses the

problem’s defined objectives.

4.3 Disaster, Transportation Network, and Recovery Process

Disaster in a transportation network is a set of disruptive conditions that hinder

connectivity, accessibility, and mobility, which leads to an extreme loss of network

functionality. The transportation network is the sole post-disaster lifeline that in

parallel grants mass mobility and provides access to essential origin and destinations

(ODs) within the affected area. Transportation networks are not only structurally

vulnerable to hazards but are also prone to cause failure for most of the

infrastructure systems and disruptions in society’s daily activities (Liu et al. 2019).

In the aftermath of a major hazard, socio-economic restoration advances linearly

with the transportation recovery rate. Therefore, successful recovery planning

contributes to society’s resilience by enhancing the recovery rate that can accelerate

the system’s serviceability during the recovery process (Zhang and Alipour 2020;

Renne et al. 2020).

Planners and decision-makers intend to respond to disasters by employing optimal

reconstruction plans to effectively and efficiently repair the damaged network and

restore it to an acceptable level of service (Renne et al. 2020; Karlaftis 2007).

Reconstruction planning of transportation networks is the outcome of a decision-

making model that prioritizes a network’s components for recovery such that it

optimizes predefined objectives. Based on their properties, objectives can be

fundamental, means, process, or strategic (see Keeney 1992). Fundamental and means

objectives are the primary objectives of a decision model (Gregory and Falling 2002).

Objectives of transportation recovery planning can be classified based on the

characteristic of the i) performance of the network and ii) performance of the

recovery process (Rozenberg et al. 2019; Benavidez et al. 2018; Zhang et al. 2017;

Quarantelli 1999). Performance of the network includes measures that maximize

links or the network’s capacity in sustaining the traffic flow, quality of the level of

service, connectivity of the network, and providing access. Performance of the

IV- Decision attributes of DRPTN

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recovery process contains variables that impact the network’s functionality while

minimizing recourses such as duration, budget, workforce, and equipment, leading

to an improved recovery rate.

Attributes of a DRPTN problem measure the achievements of the planning objectives

mainly to maximize mobility and accessibility in a network or the efficiency and

effectiveness of the recovery process. While mobility is attached to the traffic

characteristics of a network, accessibility considers characteristics of links in a

network. Measuring mobility, attributes such as link capacity, link flow, travel time,

and Average Annual Daily Traffic aim at facilitating the movement of users within the

network considering the quality of traffic after disasters (Zhang et al. 2017; Bin et al.

2009; Vugrin 2014; Zhang et al. 2019). Accessibility is driven by the adjusted travel

demand on the network under post-disaster circumstances and aims to provide

access to nodes or other links and maintain the network’s connectivity. As such

attributes, access to service-providing nodes, centrality measures, and network

topology have been used in DRPTN literature (Zhu et al. 2020; Helderop and Grubesic

2019; Aydin et al. 2018; Shiraki et al. 2017; Chang 2003).

Efficiency and effectivity of a recovery operation irrespectively represent the impact

of recovery on users and resources. Effectivity is the property of recovery operation

concerning the impacted users of the network, which includes attributes such as

integration of network travel time improvement and traffic flow, affected population

and travel delay, or social vulnerability and travel delay cost (Konstantinidou et al.

2019; Ho and Sumalee 2014; Unal and Warn 2015). The aim is to maximize the

resulting improvement of network performance to serve a higher number of users,

or a specific class of users, that are beneficiaries of the recovery operation. Efficiency

considers resources such as time, equipment, work crew, and budget to provide the

planning with low-cost, high-impact solutions and enhances the recovery rate. Some

instances of the representing attributes for recovery efficiency are unrestored ratio,

integration of travel cost and recovery duration, improved network performance in

recovery duration, or improved network travel time per available recovery work

units (Zhang 2017; Bocchini and Frangopol 2012; Zamanifar and Seyedhosseini

2017; Sato and Ichii 1995; El Anwar et al. 2016).

Disaster Recovery Planning of Transportation Networks; Problem structuring and decision attributes

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4.4 Knowledge Gap and Motivation

In general, research points out that part of the decision analysis literature neglects

the role of problem structuring, including establishing a tenable set of attributes as a

prelude to developing a decision-making model (Cochran et al. 2011; Belton and

Stewart 2010; Corner et al. 2001). In particular, the focus of the DRPTN literature is

mainly on the problem-solving step of the decision modeling, while an insufficient

attempt has been made to establish attribute sets of DRPTN models (Zamanifar and

Hartmann 2020). In this study, we intend to flip the focus and recognize the

significance of problem structuring in terms of establishing tenable attributes for the

sensitive and critical problem of DRPTN.

A few studies in the infrastructure disaster recovery field suggest attributes and

decision factors (e.g., Martins et al. 2019; Carreño et al. 2007; Ghavami 2019;

Contreras et al. 2018). While several studies discuss that some of the existing

attributes of decision problems are likely subjective, intuitive, or adopted without

contextual justification (e.g., Tiesmeier 2016; Xiaofei et al. 2018), it is critical for the

model’s quality that attributes are the result of a reliable structured approach. This

criticality increases in disaster recovery planning research due to 1) extreme socio-

economic stakes, 2) the challenge in the model validation due to the non-

observability of the problem, and 3) the existing gap in DRPTN literature to formalize

the attribute selection process. On the ground of supervising subjectivity in this

sensitive and critical context, a formal approach for establishing effective and

comprehensive decision factors for DRPTN problems is an imperative need. Bridging

this gap, we formulate and solve a choice problem of selecting among a finite number

of attributes inputted by the literature and experts of the field. Finally, the selected

case study also justifies the necessity of this research. The existing hazard exposure

and vulnerability in the study area, as well as available empirical knowledge among

local decision-makers due to experience of confronting multiple hazards in

transportation networks, motivated us to perform the analysis in the Tehran context.

Iran is a hazard and disaster-prone country. Tehran, in particular, is a metropolitan

area developed over an asymmetric complex lifeline network and intricately

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interwoven infrastructure system (Monajem and Nosratian 2015). The city consists

of structurally and socially vulnerable urban environments. On the one hand, fragile

resilience capacities, ripple effect-prone civil systems, and fragmented coordination

in crisis management that is associated with stiff decision-making flow raise the

likelihood of exposure of the urban area to transforming hazards to disasters. On the

other hand, given the experience of confronting multiple disasters, there are valuable

insights and empirical knowledge among the local disaster managers and city

planners, making it a reasonable case for our study.

4.5 Methods and the Research Design

To follow a systematic attribute selection methodology, we adopted the framework

introduced in the previous chapter. Figure 4.1 provides a summary of the research

approach. We followed a disciplined framework to extract, evaluate, and select

DRPTN attributes. To build a screening-utility choice model, we integrated three

main components of prescriptive decision modeling, including problem structuring,

preference elicitation, and evaluation /aggregation. This section demonstrates how

we followed the steps to accomplish the tasks of Figure 4.1.

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Figure 4.1: Schematic consecutive of the research framework.

4.5.1 Problem Structuring

In the first step, we identified four objectives of a DRPTN model, as discussed in

section 4.3. Objectives are organized into means and fundamental objectives

representing the primary objectives of the at-hand DRPTN problem shown in Figure

4.2. Fundamental objectives seek to achieve targeted properties of the network, while

means objectives aim at targeted properties of the recovery operation.

Figure 4.2: The structure of objectives of DRPTN problems.

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126

In the second step, we identified a list of DRPTN-related attributes as the alternative

pool of the model. To do so, we used attributes suggested by both literature and

disaster management experts to obtain an expanded list of candidate attributes.

Extracting literature-based attributes is based upon our previous work (Zamanifar

and Hartmann 2020), where we performed a content analysis within DRPTN

literature that led to 34 unique decision attributes. Besides, we conducted a survey

of 23 experts working in Tehran’s crisis management organizations, which resulted

in ten additional attributes after excluding duplicated items (total: 27 unique

attributes). We provided experts three questions with a beforehand description of

the survey and presentation of a disaster scenario. The first question was to list three

main important links with the highest priority of recovery operation in the local

traffic zone for which they are responsible. Second, we asked them that based on

what attributes those links have been selected. Accordingly, the third question was:

for a new network with which they are unfamiliar, what information do they need to

plot a possible recovery plan to prioritize links? The first question was to establish a

degree of familiarity with the problem and promote case-based deep thinking.

Finally, we extracted attributes that experts mentioned in the questionnaire

responding to the second and third questions. Moreover, 13 attributes have been

added to the alternative pool as the product of redefining attributes during the

evaluation process. Table 4.1 shows the distribution of the population of the

alternative pool based on the source of inclusion.

Table 4.1: Sources of attributes as the input of the decision model.

Share in the alternative pool

Redefined during the evaluation

22.8%

Survey of DRPTN experts

17.54%

Literature of DRPTN

59.64%

In the third step, we adopted existing evaluation factors for attributes as “properties

of a good attribute” (Keeney 1992) according to what literature on MCDA problem

structuring has been suggesting. Besides, we distinguished between properties of a

desired single attribute in isolation and attributes in a set. On this ground, while

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seven factors evaluate attributes (members), three factors evaluate the set of

attributes.

Thereafter, we divided ten evaluation factors into three decision regions with their

associated known decision rules as compensatory, non-compensatory, and optimal.

The first region is the screening region with a non-compensatory decision rule that

acts as a filtering step of the evaluation process. The screening region is responsible

for excluding attributes that i) are irrelevant to the decision context (coherency with

objective), ii) are not commensurable in a consistent manner and with a reasonable

amount of effort (operational), and iii) do not clearly compare and distinguish among

all alternatives (discriminative).

Attributes that satisfy all factors of the screening region enter the choice region. The

choice region accepts a compensatory decision rule, that is to say, a compromise

among attributes is a valid consideration. This region ensures that an attribute

receives a higher utility when first, it has a clear and unambiguous definition

(understandable). Second, it yields a reasonably certain measured value for the

respective objective (certainty). Third, it directly measures the primary objectives of

the decision problem (directness), and fourth, it represents essential characteristics

of the modeled problem (representative). Unlike the first two regions that evaluate

“individual attributes”, the third group of factors evaluates “sets of attributes” based

on an optimal decision rule. An optimal decision rule can be formulated as a

presumably ideal outcome for a set of attributes that captures the key aspects of all

objectives (completeness) while keeping the size of the attribute set to a minimum

(concise). Besides, the set should not contain a double-counting attribute (non-

redundancy), which can be expressed as the constraint of the optimal region.

4.5.2 Relative Importance of Compensatory Factors

Step four is to assign a trade-off among compensatory evaluation factors. To do so,

we used the inputs of six MCDM experts for the preference elicitation task. Experts

provide an ordinal rank for evaluation factors from the most important to least

important and adjust the distance among those sorted attributes on a visualized

slider to input their cardinal preference between each pair of evaluation factors.

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Table 4.2 shows the weights of compensatory evaluation factors.

Table 4.2: The trade-off among compensatory evaluation factors.

Compensatory

evaluation factors

Understandable

Representative

Direct

Certainty

Ordinal value

Relative importance

20.68

27.44

36.56

15.32

4.5.3 Evaluation and Value Aggregation

To measure the performance of alternatives on each evaluation factor, as the fifth

step, we held a workshop with a focus group consisting of four members of a group

of experts that previously developed the disaster recovery planning of the Tehran

transportation network. At the time of the research, three of the experts held a

Master’s degree in urban planning, civil engineering, and transportation planning

disciplines and one a Ph.D. in disaster management. The working experience of four

experts was eight, 11, 13, and 16 years with ongoing involvement in the field. As the

official decision-makers of crisis management organizations, they had direct

responsibility for and experience of the problem in question. Therefore, the DMs met

the inclusion criteria of authority, stake, knowledge, and experience that qualify them

to be considered subject-matter experts. Before the evaluation session, we

elaborated on the structure and function of the model and discussed the problem at

hand by presenting a brief disaster scenario as well as detailed descriptions and

definitions of the evaluation factors. At first, experts evaluated alternatives based on

three non-compensatory evaluation factors and assigned a binary value of 1 or 0.

Obviously, alternatives that did not pass the screening step have zero probability of

being chosen unless experts define a revised version. We then used a direct rating on

a local scale of 0 to 10, where 10 represents the best performance of the alternative

and 0 represents the worst. Accordingly, experts evaluated each alternative’s

performance based on the four evaluation factors of the choice region. In this step,

the group was also allowed to redefine the attributes that did not satisfy the

evaluation factors of the screening region. Experts collaboratively came to a

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129

consensus on the score of each alternative and reported it afterward. Consequently,

we calculated the utility of 33 alternatives of the choice region based on the input of

the focus group, the weight vector of the previous step, and the aggregation methods

introduced in the next step.

In the sixth step, we used a combination of compensatory and non-compensatory

MADM methods. We employed a version of Elimination by Aspect method (Tversky

1972) for the screening region and Multi-Attribute Value Theory (MAVT) (Keeney

and Raiffa 1976) for the choice region to aggregate DMs’ input values on the

performance of each alternative against evaluation factors as the criteria of the

decision model. MAVT is a well-axiomatized method, easy to understand, apply, and

track, which is widely discussed in compensatory MCDM literature (see, e.g., Munda

2005). Elimination by aspect is a robust yet straightforward non-compensatory

approach that follows the axioms presented with the lexicographical choice concept

(see, e.g., Fishburn 1975). It is a useful approach for managing the problem’s size and

remains true to the non-compensatory rules where the preference transitivity is not

desirable. In the seventh step, conceptual mapping of attributes based on their

generic representative value took place. Here, DMs assigned the ranked attributes of

the previous step to each representing objective to understand if attributes reflect

the expected achievements designed as goals of the decision analysis. Finally, the last

step inherits the ranked list of attributes from screening and choice regions classified

with the objective-based value tree of the previous step. In this step, the task is to

evaluate sets of attributes based on completeness, size, and non-redundancy. Non-

redundancy ensures that in the selected set, an identical value is not dually counted.

In the optimal region, the minimum size of a non-redundant attribute set that

satisfies the set’s completeness is the selected set of attributes.

4.6 Main results

4.6.1 Evaluation and Value Tree

The utility value and rank of the first 16 attributes are shown in Table 4.3. Initially,

24 attributes were excluded in the screening region based on the non-compensatory

evaluation factors. The full list of attributes of the alternative pool, the evaluation

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130

inputs, and the attributes’ aggregated utilities are available online as the

supplementary material (Zamanifar 2020) and appendix (B) of this dissertation.

Table 4.3: The first 16 ranked attributes as the outcome of the choice region and their

utility scores.

Attribute

Utility/Rank

Attribute

Utility/Rank

Access level of link to SP nodes

29.675

(1)

Connectivity to other traffic

zones

25.524

(9)

Travel time

improvement/resource

29.375

(2)

Social vulnerability*link flow

23.548

(10)

Travel delay of link *flow of the

link

28.912

(3)

Annual Average Weekly

Traffic (AAWT)

23.257

(11)

Travel time

improvement/recovery

duration

28.448

(4)

Social vulnerability* zone

travel demand

22.948

(12)

Centrality measures 

27.942

(5)

Network topology

22.787

(13)

Impact on total network travel

time

27.193

(6)

Annual Average Daily Traffic

(AADT)

22.151

(14)

East-west and north-south

connectivity

26.63

(7)

Traffic density

22.024

(15)

Link capacity

25.878

(8)

Recovery efficiency

21.969

(16)

By transmitting the ranked output of the choice region into the optimal region, the

first 16 ranked attributes are distributed through the objective-based value tree, as

shown in Figure 4.3. The assignment of attributes is based on identifying the

objectives that are measured by attributes. In our workshop, the task of assigning

attributes to their representative objective was terminated once each objective

received at least three attributes.

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131

Figure 4.3: The generic distribution of the first 16 attributes to the respective primary

objectives.

4.6.2 Recommended Set

Based on the generic distribution of attributes to their respective objectives mapped

in Figure 4.3, the focus group agreed on six attributes as the recommended attribute

set for the DRPTN model that includes: Access level to Service-Providing nodes (rank

1), Travel delay of link *flow of the link (rank 2), Travel time improvement (TTI) per

resources (rank 3), Travel time improvement per recovery duration (rank 4), Centrality

measure (rank 5), and Link capacity (rank 8). The first five ranked attributes of Table

4.3, plus capacity ranked as the 8th attribute, constitute the recommended set. Table

4.4 offers an overview of the rank, related objectives, and utility of the attributes of

the recommended set, followed by brief descriptions of the final set of attributes.

Table 4.4: Attributes of the recommended set, utility score, and their associated

objectives.

Attribute

Access level to

SP nodes

Travel delay of

link *flow of the

link

TTI/resources

TTI/recovery

duration

Centrality

measure

Link

capacity

Rank

(1)

(2)

(3)

(4)

(5)

(8)

Score

29.675

29.375

28.912

28.448

27.942

25.878

Objective

Accessibility

Effectivity

Efficiency

Accessibility

Mobility

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132

(1) Access level to Service-Providing nodes- Service-Providing (SP) nodes are

critical sources and sinks that produce emergency travel demand to which safe and

fast access is necessary for the social system after a disaster. Service-providing nodes

deliver critical services and commodities such that delays in their functionality or

administrative operations execute adverse impacts on the economy, daily life, civil

protection, and social wellbeing. All those origins and destinations fall in the category

of nodes to/from which travel demand is generated due to the post-disaster

emergent condition. This attribute measures the capability of links in providing

access to the location of SP nodes on the network (Ulusan and Ergun 2018; Miller et

al. 2003).

(2) Travel time improvement per resources- This attribute refers to the impact of

a link reconstruction on network travel time given the resources required to

implement such a recovery. Network travel time is a time-based metric for the

network performance, which can account for the impact of the network’s physical

deterioration, as well as for the possible variations of travel patterns in a post-

disaster setting (Kostanisou et al. 2019). The attribute represents the amount of

machinery, work units, or monetary resources that have to be assigned to achieve a

certain improvement of network travel time.

(3) Travel delay of link * link flow- This attribute calculates the travel delay that a

link causes to network travel time during closure or reduced functionality,

integrating to the amount of the traffic volume that the link sustains. Similar to the

previous attribute, this composed attribute indicates the importance of a link for

network travel time, but it also includes the magnitude of users impacted by the link’s

dysfunction. However, unlike the travel time improvement, it computes the disutility

that closure or reduced capacity of a link dictates to the travel time on the serving

network.

(4) Travel time improvement/recovery duration- As a metric of impact per

consumed time, this attribute is a simple form of representing the temporal rate of

recovery that implies the impact of links’ reconstruction in a “recovery duration–

travel time improvement graph”. The attribute directly measures the extent to which

the recovery of a link has an influence on achieving travel time improvement in a

Disaster Recovery Planning of Transportation Networks; Problem structuring and decision attributes

133

specific unit of time to represent the recovery operation’s efficiency.

(5) Centrality measures- Centrality measures indicate the topological merit of a link

in a network regardless of the traffic flow. In the context of graph theory and traffic

engineering, centrality importance refers to attributes that measure the degree of

connectivity or topological importance of a link within the embedding network.

(6) Link capacity- A definition of capacity is: “the maximum sustainable hourly flow

rate at which vehicles reasonably can traverse a point or a uniform section of a lane

or roadway during a given period under a prevailing roadway, environmental, traffic,

and control conditions” (TRB 2000). Link capacity determines each link’s ability to

carry the traffic as a measure of the mobility performance of a link.

4.6.3 The Selected Set and DRPTN Literature

The link capacity attribute has been used in 17.5 % of the reviewed DRPTN studies

(Zamanifar and Hartmann 2020) as a flow-independent parameter of a

transportation network (e.g., Zhang and Miller-Hooks 2015; Bin et al. 2009; Vugrin et

al. 2014). However, several other studies suggest flow-dependent attributes such as

free-flow speed, density, Average Daily Traffic, or Annual Average Daily Traffic as a

representative metric of network mobility and ability of links to maintain the traffic

load or to provide access (e.g., Ho and Sumalee 2014; Hackl et al. 2018, Sato and Ichii

1995; Zhao et al. 2020, Sohn 2006). Similarly, the attribute Travel delay of link *flow

of the link integrates “traffic flow,” which is argued favorably by Chang (2003), while

Chang and Nojima (2001) suggest a limited application of flow-based measures after

a disaster. Two attributes of the recommended set incorporate “travel time” as a

recognized factor in estimating the performance of perturbed transportation

networks (e.g., Orabi et al, 2009; Kepaptsoglou et al. 2014; Liberatore et al. 2014).

Furthermore, the attribute Travel time improvement per recovery duration represents

the recovery rate that is aligned with many DRPTN studies and perhaps is the most

commonly agreed attribute in the DRPTN model (e.g., Zhang 2017; Bocchini and

Frangopol 2012; Sato and Ichii 1995; El Anwar et al. 2016).

Unlike the attributes mentioned above, centrality measure has not been broadly used

in DRPTN literature. Among 46 reviewed DRPPT studies, we could identify two

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134

studies (Ulusan and Ergun 2018; Merschman et al. 2020) that adopt the centrality

measure as a decision attribute in DRPTN optimization problems. Furthermore,

although the attribute access to SP nodes is initially inputted to the evaluation process

by DRPTN literature, only 12.5% of the DRPTN studies included the level of access to

critical facilities.

4.7 Sensitivity Analysis

We performed a local preference sensitivity analysis to understand how the resulting

ranks of attributes are sensitive to supervised parametric variations in the weighting

vector (Bertsch et al. 2007). This analysis reveals the range of robustness of the rank

of the prioritized attributes based on the change of each evaluation factor’s relative

importance coefficient at a time (Li et al. 2013). Therefore, 𝜌 is defined as a unitary

preference variation coefficient that indicates the domain of change for each weight

of four compensatory evaluation factors of certainty, directness, understandability,

and representativeness. The corresponding utility of respective 𝜌 in both upper and

lower bound for ten schemes from -50% to +50% was calculated and new rankings

were analyzed. Table 4.5 reports the rank reversal of the first eight attributes to

demonstrate the change in the rank of the six selected attributes of the final set. The

rank reversal locations are highlighted, and the border of rank discrepancies is

identified for each 𝑅𝑖 denoting the original rank of attributes.

Table 4.5: (Next page) the rank reversal and thresholds of rank sensitivity to weights

of evaluation factors for attributes of the selected set

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135

Evaluation factors

Certainty

Directness

Ranked attributes

𝑅1

𝑅2

𝑅3

𝑅4

𝑅5

𝑅6

𝑅7

𝑅8

𝑅1

𝑅2

𝑅3

𝑅4

𝑅5

𝑅6

𝑅7

𝑅8

Ratio

New rank under unitary preference variation

𝝆𝟎.𝟏

−

𝝆𝟎.𝟏

𝝆𝟎.𝟐

−

𝝆𝟎.𝟑

−

𝝆𝟎.𝟑

𝝆𝟎.𝟒

−

𝝆𝟎.𝟒

𝝆𝟎.𝟓

−

𝝆𝟎.𝟓

Evaluation factors

Understandability

Representativeness

Ranked attributes

𝑅1

𝑅2

𝑅3

𝑅4

𝑅5

𝑅6

𝑅7

𝑅8

𝑅1

𝑅2

𝑅3

𝑅4

𝑅5

𝑅6

𝑅7

𝑅8

Ratio

New rank under unitary preference variation

𝝆𝟎.𝟏

−

𝝆𝟎.𝟏

𝝆𝟎.𝟐

−

𝝆𝟎.𝟑

−

𝝆𝟎.𝟑

𝝆𝟎.𝟒

−

𝝆𝟎.𝟒

𝝆𝟎.𝟓

−

𝝆𝟎.𝟓

IV- Decision attributes of DRPTN

136

For the evaluation factor of certainty, the final rank of eight attributes changes when

the weight coefficient increases or decreases by ±10%, whereas, for the first three

ranked attributes, this variation leads with the change of ±30% in the factor’s initial

weight. Under the preference change of the understandability factor, the overall rank

of attributes exhibited a relatively insignificant alternation while the order of

attributes remains utterly stable for the representativeness factor. Therefore, Table 4-

5 shows that the sensitivity of attributes’ ordinal rank to the weights of those factors

is remarkably low, which is logically predictable, as the same holds for the

diversification of assigned values for the performance of attributes within the

evaluation process. Furthermore, no rank reversal is observable for the first three

attributes when we applied a series of variations to the weight of the directness factor.

The impact is, however, noticeable within the range of rank four to eight, should the

weights increase or decrease by ±30%.

In general, a moderate rank reversal is noticeable only for the certainty factor

corresponding directly to the diversification of DMs’ assigned values in the

evaluation process. Therefore, the analysis suggests that considerable information is

preserved in the assigned values to the certainty factor; thus, the certainty of an

attribute could have attained higher relative importance for the participating DMs. In

total, a significant shift in the rank of attributes or extreme rank reversal was not

detected. This can suggest that, concerning preference values, the outranked

outcome is relatively robust. One should note that this analysis cannot be safely

counted as hard evidence for the general robustness of the final results since this

behavior is not unconventional for a prescriptive model with a flat hierarchy of

evaluation factors and no inflection point in the linear weighting vector that allow an

undeviating transition of preferences to the aggregation model. Nevertheless,

findings of the performed analysis do provide an understanding of how non-

deterministic inputs could impact the rank of attributes and what uncertainty

thresholds could be drawn.

Disaster Recovery Planning of Transportation Networks; Problem structuring and decision attributes

137

4.8 Discussion

4.8.1 Analysis of the Attribute Set

Access level to SP nodes obtained the first rank in the choice region. As a universal goal

for every crisis, restoring society to a normal condition is a logical target for DRPTN

problems. Therefore, the accessibility index to nodes such as critical facilities was

expected to obtain the highest utility and establish itself as the main concern of DMs.

The attribute Travel time improvement/resources aims at providing low-cost high-

impact solutions after a disaster, which renders the attribute an attractive option for

DMs. Decision-makers also emphasized the significance of certainty about available

and dispensable resources after disasters and indicated that the efficient use of

resources is of utmost importance in their planning approach toward prioritizing

recovery operations. Travel delay of link *flow of the link measures the effectiveness

of the recovery operation. The focus group was leaned toward solutions that impact

a larger amount of the population and satisfy a broader range of users to ensure the

effectiveness of recovery operations. Broadening the extent of public satisfaction was

also a motive for DMs to be interested in this attribute. The attribute of Travel time

improvement per recovery duration represents the progressive performance of

recovery in units of time. Clearly, an incremental recovery rate, i.e., the slope of the

duration–improvement graph, yields reaching an improved state of the network

promptly. DMs stated that it is not only important to shorten the period that the crisis

impacts the transportation network but also to generate psychological comfort when

users observe short-time progressive shocks to the system which can project a timely

elevation of network quality level.

Centrality measure is a contextually relevant and practical attribute after disasters

since a known pre-event traffic stream will not remain the same under post-event

circumstances, and overall connectivity of the network pertains to restoration of

centrality-centric important links. The certainty of performance of centrality

indicators was the key feature of this attribute’s favorability since it is less likely that

the topological position of a link varies after a disaster compared to the same

probability for the traffic flow. Another justification for employing this attribute was

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138

the extent that centrality importance contributes to maintaining connectivity in a

network since it is reasonable to assume that the degree of connectivity of a network

with restored central links is meaningfully higher than a network that is rehabilitated

without considering centrality features of links. Link capacity with the eighth highest

utility represents the objective of mobility. In the post-disaster setting, prioritizing

links based on the traffic capacity improves the network’s performance in operating

post-event travel demand. DMs’ main motivation was to accommodate higher travel

demand into the network in the early stages of a recovery process by accelerating the

recovery of high-capacity links. It is a reasonable assumption in post-disaster

conditions that users are more inclined to choose roads with higher capacity to avoid

undesirable congestion in the small streets. Although capacity received a medium

score for directness since it does not take into account any characteristic of disaster

condition, perhaps for the same reason, it received the full score of the certainty

factor. In fact, both centrality and capacity are important indices of links concerning

mobility and accessibility regardless of the perturbed condition of a network. While

they do not represent characteristics of a disrupted network, their resulting lower

score for directness and representativeness is compensated with a higher score in

certainty and understandability of attributes.

As a set, the selected attributes cover the concerns related to the problem and ensure

that objectives are completely measured. Although each attribute deems to be

individually an important factor, to address all defined objectives, the implication of

the recommended attributes is meaningful only by remaining as a set. Within the case

study domain, results suggest the feasibility of following a structured decision

framework for selecting decision attributes of a DRPTN problem. The carefully

collected, systematically analyzed, and critically evaluated attributes allow the

harnessing of the knowledge of subject-matter experts in the context of DRPTN.

Therefore, DRPTN research can use the outcome of this research as the input of the

problem structuring phase of newly developed disaster recovery models.

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4.8.2 Practical Implications

Determining decision attributes of disaster recovery planning is the hardest yet most

important task in a decision modeling process of a DRPTN problem. This study

harnessed DMs’ knowledge as subject-matter experts for identifying attributes of

DRPTN through a formalized systematic evaluation and selection process. On this

ground, while making decisions on the priority of recovery operations, we suggest

that disaster managers consider using the proposed key attributes to evaluate the

consequence of choices on recovery options. Based on the description of the six

selected attributes, should this set be utilized in a DRPTN model, a recovery strategy

will receive a higher utility if it:

1) Has a higher impact on reducing travel delay and affected users;

2) Requires fewer amounts of recovery recourses for improving travel time;

3) Provides a wider access level to the service-providing places;

4) Prioritizes the links with higher capacity;

5) Has a higher centrality importance;

6) Leads to an earlier recovery impact on network travel time.

According to Table 4.4, the six key attributes represent the four defined objectives.

Hence, a formulated plan based on the recommended set potentially maximizes the

impact of recovery while covering a wide range of users to expand the threshold of

resilience. Additionally, it allows the prioritizing of links that facilitate access to

critical nodes and a maximizing of the capacity of network mobility. However, it

might be cumbersome to formulate an optimization problem that can incorporate all

four objectives and provide a feasible solution space with reasonable computational

complexity. Therefore, attributes of the set can also be used individually if the goal of

the planning is to address one or more of those objectives. For example, as Figure 4.4

demonstrates, to focus on maximizing the efficacy of post-disaster recovery

operations, the attribute Travel delay of link *flow of the link is recommended. For

maximizing the efficiency of recovery planning, two attributes Travel time

improvement per resources and Travel time improvement per recovery duration, form

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140

a representative and complete set. At the same time, DMs need to incorporate the

attribute Access level to SP nodes if maximizing network accessibility is intended as

well.

As a remark for DRPTN modelers, the resulting attribute set suggests that the

integrating of parameters to develop as Keeney (1992) defined constructed

attributes is required to address the DRPTN primary objectives. For instance, the

attribute Travel time improvement/recovery duration underscores that “recovery

duration” would be a practical parameter only if it portrayed the network

performance progression per consumed time and indicated a ratio of recovery

progress in terms of its impact on technical characteristics of the network. Similarly,

regarding the attribute Travel time improvement /resources, single traffic properties

such as travel time will be more effective when integrated with contextual

characteristics of recovery operations. With respect to the attribute Travel delay of

link *flow of the link, disaster managers should note that a road with higher traffic

volume is not necessarily more important, but attention should be paid to the extent

to which this traffic volume is vulnerable to travel delay due to the damage at a

network level. Finally, it is reasonable to believe that post-disaster travel demand

patterns will not remain as the pre-disaster condition. Hence, centrality measures, as

a flow-independent attribute, would perhaps be a robust representative of links’

merit. The proposed attribute set would be useful for disaster managers to employ

as key factors for developing recovery planning decision support systems or as key

performance indicators for evaluating successful recovery and resilience plans.

4.9 Limitations and Future Research

Finally, to point out possible limitations of the research approach, one should note

that the evaluation task within the model is one of the subjective parts of the decision

process as an inherent feature of all decision models. Consequently, the selection of

the attribute, in the end, always depends on experts’ opinions and their collaboration

structure, which is, to a great extent, influenced by various factors such as their area

of expertise, the socio-geographical factors, degree of availability cascade effect,

availability heuristic bias, herd behavior, working memory capacity, their stake and

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141

knowledge. Therefore, the concern over the generalizability of the result is valid.

However, the systematic framework generates tractable outcomes that make it

possible to locate where exactly the subjectivity might influence the evaluation

process. The model also promotes creative and critical thinking and provides ground

for collaborative decision-making, as we evidentially observed during the workshop.

Therefore, it is not absolutely irrelevant if we assume that the suggested decision

recommendations offer meaningful insights and inference for possible attributes of a

universal DRPTN problem. In the meantime, future research is needed in various

geographical contexts to re-implement this research in different urban settings.

In this research, we incorporated the input of the focus group, the survey of experts,

and DRPTN literature as three sources to fill the alternative pool. However, it still falls

short in covering the contributions of a broader range of stakeholders. Since the

outcome is as complete as the alternative pool, it is important to provide a so-called

expanded complete list of attributes, including experts, literature, decision-makers,

actors, and all stakeholders. Obviously, the completeness of the alternative pool

significantly escalates the size of the problem and the likelihood of exposure to bias

and error accordingly. Moreover, a further enhancement could be the possibility to

reduce the number of attributes in the initial alternative pool. During our research,

we did not look into such possibilities to logically analyze attributes to understand

whether several attributes can be effectively subsumed into a single one.

4.10 Conclusion

While urban systems are encountering an unprecedented risk of climate-induced and

natural hazards, it is of paramount significance to develop decision support systems

that pave the way for well-informed collaborative decision-making. In order to

develop such a DSS, modelers should feed the decision models with tenable and

plausible decision attributes resulting from a reliable formal selection process. Based

on this premise, we used a new modeling paradigm to aid decision-makers in

selecting attributes of a DRPTN model of Tehran. The aim was to formally extract the

knowledge of subject-matter experts as DMs about concerns and values in the

reconstruction and recovery of transportation networks after disasters. DMs

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proceeded to evaluate 57 attributes through multi-stage yet non-hierarchy three

sequential decision regions. Six key attributes were identified as the recommended

set to cover the main concerns of the decision problem based on the primary

objectives. The recommended set is supposed to be complete and non-redundant

with compromise in conciseness. Additionally, all attributes individually obtained a

relatively high utility, satisfying representativeness, directness, unambiguity, and

certainty of measure. The model-driven attribute recommendation allows decision-

makers to choose a more contextually related set to the decision environment’s

specific conditions, such as available local data, computational power, objective

preference, and certainty threshold. Given the circumstances under which other

attributes with the trajectory utility fit DRPTN model requirements, the set can adapt

accordingly. The implementation of the framework was successful in harnessing

collaborative experts’ input in a structured manner. However, it by no means

presents an assertive uniform prescription, but indeed offers the ability to track the

decision process, organized and critical thinking, and an enhanced quality of choice.

While the attribute set is defined, an emergent challenge is to formulate a problem

that can be solved with a reasonable computational cost. As we pointed out in the

discussion section, using the recommended set of attributes in a disaster recovery

planning decision model is expected to provide effective and efficient solutions that

maximize mobility and accessibility in the network. Therefore, we call for studies that

formulate and solve a decision problem by integrating the decision attributes

introduced in this research.

Disaster Recovery Planning of Transportation Networks; Problem structuring and decision attributes

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Chapter V

CONCLUSION

“We are in great haste to construct a magnetic telegraph from Maine to Texas; but Maine and

Texas, it may be, have nothing important to communicate... We are eager to tunnel under the

Atlantic and bring the old world some weeks nearer to the new; but perchance the first news

that will leak through into the broad flapping American ear will be that Princess Adelaide has

the whooping cough.”

Henry David Thoreau, Civil disobedience, (1849)

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5 Conclusion

5.1 Summary and Main Findings

This research began with a comprehensive and systematic literature review that

sought to identify knowledge gaps in the DRPTN decision modeling process.

Optimization-based DRPTN modeling was considered as a process comprised of four

primary phases: problem definition, problem formulation, problem solving, and

model validation. For each phase, certain challenges and opportunities were

articulated, as were suggestions concerning how the identified gaps could be

overcome. In order to address the knowledge gaps related to the lack of problem

structuring in DRPTN models, I then developed a prescriptive decision aid

mechanism that can harness experts' knowledge base on the value of DRPTN decision

attributes and prescribe an attribute set. Accordingly, the process of attribute

evaluation and selection was formulated as a screening-choice utility decision model.

To implement the framework in a real-world DRPTN problem, I collected expert and

literature-based potential attributes to develop an alternative pool by using a survey

that contained results from 23 senior experts and content analysis of 46 DRPTN

studies.

In the next step, I extracted evaluation factors from literature related to decision

analysis and problem structuring that were subsequently utilized in a workshop to

appraise the attributes of the alternative pool. Next, the challenge was to determine

the relative importance of compensatory evaluation factors based upon six MCDM

experts' opinions. Once the set of alternatives, evaluation factors, and their relative

weights had been established, I held a focus group workshop featuring four disaster

managers, which included several tasks to implement the framework, and observe its

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performance. The newly developed framework consists of innovative integration of

compensatory and non-compensatory aggregation methods within a sequential

discrete three-stage evaluation process, employing ten evaluation factors. During the

workshop, maximizing mobility, accessibility, recovery efficiency, and recovery

efficacy were considered the primary objectives. The experts were then asked to

evaluate and rate individual attributes within two stepwise decision regions based

upon region-specific evaluation factors. Each decision region had its own decision

rules. The first decision region submitted to a non-compensatory decision rule,

wherein Elimination by Aspect was used to screen the candidate attributes. The

second decision region operated under a compensatory decision rule for the task of

direct point allocation. When the evaluation process of single alternatives had been

completed, I then calculated the utility of attributes using MAVT, and presented the

focus group with the resulting ranked list of attributes. After that, the evaluation

within the third decision region was conducted with an optimal decision rule by

developing a value tree as a concept map of objectives and their respective

representative attributes. The focus group then selected a set of attributes based

upon the sorted attributes and the value tree to satisfy the three optimal region's

evaluation factors. The after-workshop analysis included a feedback session using a

survey with two direct questions, an analysis of observations during the evaluation

process, an open discussion with users, sensitivity analysis, and entropy information

analysis of the factors, as well as a typological and descriptive analysis of the final

attribute set. The chosen attributes were also compared to the working attributes

that the decision-makers selected for the same context in an unaided procedure. The

findings of the research have been reported in three sections, which are outlined in

detail below.

The findings of my gap analysis suggest that existing DRPTN models face critical

challenges in adopted decision attributes and introduced a lack of theoretical

argument for inclusion of attributes and the absence of a formal process that justifies

and supports the selection of decision factors. Furthermore, the inclination towards

using meta-heuristic solving algorithms where linear programming could provide a

globally optimal solution, as well as the general absence of explicit or implicit

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justification of solving methods (e.g., convexity, linearity, or complexity analysis of

mathematical programming), characterized the problem-solving phase of DRPTN

modeling. However, the existing user-friendly tools supporting meta-heuristic

solving algorithms, the perceived novelty associated with their applications, and the

ability of these methods to perform an exhaustive search within a reasonable

computational cost make it an interesting approach, especially where non-experts

are engaged with optimization models. In the problem formulation phase, limitations

in integrating traffic management measures and post-event travel demand models

into the formulation process of network recovery were highlighted. Finally,

challenges in validating DRPTN models in terms of presenting a benchmark or level

of confidence to support the reliability of outcomes rounded out the reported gap

analysis. The first section's conclusion argues that DRPTN research needs to raise

awareness of method-rich but methodology-poor syndrome as a persistent challenge

for disaster recovery models.

The second section reported on findings related to the developed attribute selection

methodology and the framework. Accordingly, the framework was designed as a

toolkit for processing experts’ input as relates to selecting decision attributes and

framing a disciplined decision process. The multi-stage yet non-hierarchical

structure of the framework allowed for a critical and thorough evaluation of

candidate attributes to be undertaken in a relatively user-friendly manner. Users

were able to systematically evaluate attributes and collaboratively produce a ranked

list of attributes, as well as the final selected set. During the implementation of the

proposed methodology, it was possible to observe that the framework could act as a

tool to extract DMs’ knowledge and help in the isolation of the elements of the

decision context that are most relevant to the problem. Based upon observations of

the discussion developments in the workshop and the position of the certain

attributes in the final ranking, the embedded evaluation mechanism facilitated

critical and creative brainstorming, thereby fostering the incorporation of available

knowledge sources. Therefore, as the framework's output, the recommended set is

the result of a systematic process and collaborative decision-making, and

consequently offers a set of attributes for both practice and research. Further, the

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model-driven attribute selection process can also be adapted to the specific

conditions of the decision environment, such as locally available data, computational

power, objective preferences, and certainty thresholds. Given the circumstances

under which other attributes with trajectory utility fit DRPTN model requirements,

the set can be adapted accordingly. Therefore, the approach employed in this

research paper enables informed and flexible decision-making for the selection of

tenable attribute sets. It is reported in chapter three that more attributes are

obtained from the literature. However, this does not suggest any meaningful insight

concerning the framework's performance since it can be a random event or only

because the process initially started with extracting attributes from the literature,

and attribute sources did not have identical numbers in the alternative pool.

Nevertheless, I have not drawn any conclusion based on this observation. The idea is

to maximize the total number of relevant attributes in the alternative pool. Although

extracting attributes initially started with literature, in the evaluation process, all

attributes have been presented together as a single alternative pool, including

attributes extracted from experts and literature. The argument developed in chapters

three and four concluded the framework's satisfactory performance based upon the

evaluation of the outcome, the discussed characteristics of the framework, and users'

feedback.

Finally, decision-makers were able to select six attributes to be included in Tehran

road network disaster recovery planning. These attributes included 1) access level to

service-providing nodes; 2) integration of link travel delay and traffic flow; 3) travel

time improvement per recovery duration; 4) travel time improvement per resource;

5) centrality measures, and 6) link capacity. The recommended set is intended to be

concise, non-redundant, and complete. Additionally, all six attributes obtained a

relatively high utility value, satisfying the criteria of representativeness, directness,

unambiguity, and certainty of measure. The analysis of the results discussed in

chapter three suggests that the framework leads to improved quality of the attributes

compared to the selected set in an unassisted manner. This claim may need further

evidence to be thoroughly validated. Nevertheless, if it is not possible to compare the

quality of outcome attributes from two different processes, the comparison of the two

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processes that yield the attributes is still a viable option. In the light of sufficient

insights that could indicate the quality of one process over another, it is unwise to

deny the improved quality of output only because the two sets of outcomes are too

qualitative to be compared.

The sensitivity analysis confirms that the outranked outcome is relatively robust with

regard to the assigned preferences, although given the number of evaluation factors

and their single hierarchy level, it was an expected outcome from such an analysis.

This argument was also supported by information entropy analysis. Sensitivity and

information entropy analyses were both aligned in suggesting sensitivity and

information preservation in the “certainty” evaluation factor. This result supports the

hypothesis that participating DMs prioritized concerns about the uncertainty

associated with attribute values for each alternative.

As was concluded in chapter four, using the recommended set of attributes in a

disaster recovery planning decision model is expected to provide effective and

efficient recovery solutions that maximize mobility and accessibility in the affected

network. One should note that the completeness of the attribute set is defined based

on the determined objectives for this specific case study and not all aspects and

dimensions of a general disaster recovery process. Based upon the description of the

six attributes, a recovery strategy will have a higher utility when it meets the

following criteria: 1) Has a higher impact on reducing travel delay and affected users;

2) Requires fewer recovery recourses for improving travel time; 3) Provides a wider

access level to the service providing places; 4) Prioritizes the links with higher

capacity; 5) Has higher centrality importance, and 6) Leads to earlier recovery impact

on travel time.

Finally, the recommended set does not claim universal validity, nor does it constitute

a uniform prescription for DRPTN models, as it is utter context-dependent. Instead,

the framework offers the ability to track the decision process, organizes and

facilitates critical and collaborative thinking, and presents an enhanced quality of

choice. The possibility of involving cognitive biases related to preference elicitation,

value assignment, and group decision-making cannot be dismissed. To better

understand the quality of the developed attributes, future research is needed.

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Nevertheless, it is reasonable to assume that the systematic attribute selection

process allows analysts to track and locate where subjectivity might influence the

evaluation process.

Finally, there is no “correct” attribute, but some sets of attributes could be more

indicative of the objectives they are supposed to represent and more operational for

the intended application of the decision model at hand. If we take the association of

a model’s outcome with the quality of its attributes as a given, investing in selecting

reliable attributes is a rational choice. As Ralph L. Keeney once wrote, "the selection

of an attribute is a decision" (Keeney 2007). Therefore, a decision aid mechanism,

such as the framework proposed in chapter three, can increase the odds of arriving

at useful or better attributes. Essentially, the path toward a better attribute can be

paved by following a systematic, transparent approach with the added value of

allowing for collaborative decision-making, creative thinking, and structured experts'

tacit knowledge elicitation.

5.2 Contributions

Assuming that “improved decision structuring will improve the quality of the

decision outcome” (Corner et al. 2001), the findings contribute to the construction of

more reliable DRPTN models and informed decisions for recovery of transportation

networks in the aftermath of disasters. The contributions can be grouped as follows:

1) gap analysis; 2) developed framework; and 3) suggested attributes. First, the gap

analysis discussed in chapter two is an original investigation of problem structuring

and methodology of optimized DRPTN models that offers perspectives and

suggestions regarding how to supplement approaches that mainly focus on optimizer

algorithms. Second, the framework presented in chapter three is designed to bridge

the knowledge gap in DRPTN decision analysis problem structuring and serve as a

means for 1) structuring knowledge; 2) communicating key information; 3) analyzing

the extracted knowledge; and, finally, 4) facilitating the selection and evaluation

process of attributes. The innovative design of the framework reduces the complexity

and cognitive burden of a model, while still including ten evaluation factors for

thorough and critical evaluation that also serve to expand the capacity for

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inclusiveness in accepting input alternatives. Third, the selected attributes

introduced in chapter four are the result of having provided a systematic strategy for

channeling experts’ knowledge toward selecting a reliable and calibrated attribute

set. The following subsections summarize the contributions and originality of this

research with regard to each of its stated objectives.

5.2.1 Contributions toward Meeting Objective 1

The findings related to the first objective open up a new discussion on the application

of optimization methods in low-validity decision environments, as well as the

application of non-deterministic optimizers in exploring the solution space of DRPTN

models. These findings challenge the existing approaches to selecting attributes and

validation of models within the reviewed papers from the existing literature. This

research also offers suggestions for all four phases of DRPTN optimization

programming. Notably, this research answers pressing questions regarding

necessary improvements in developing optimized DRPTN decision models. The

identified gaps feature important areas of optimization modeling in the context of

disaster recovery that could contribute to the improvement of future DRPTN models’

performance. The efforts add to our collective knowledge of the application of

optimization programming and decision modeling in the disaster management

context, and advance the understanding on decision modeling for recovery planning

of critical infrastructures. At the same time, this work poses the following question:

to what extent the lack of formalized problem structuring can refute the validity of

existing optimization models, and what would be the uncertainty threshold for

decisions in the context of DRPTN? The following overview outlines this research’s

contributions and originality related to meeting Objective 1.

The presented findings, research design, and arguments in chapter two:

▪ Provide a holistic, systematic literature review of DRPTN studies with respect

to the methodological application of optimized decision models in the DRPTN

context and its problem structuring;

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▪ Approach the DRPTN optimization programming as a process constituted by

four phases of problem definition, problem formulation, problem-solving, and

model validation;

▪ Identify the decision factors of DRPTN suggested by related studies;

▪ Investigate complexity and convexity analysis within the DRPTN models;

▪ Review the verification and validation process of the selected DRPTN models;

▪ Analyze the correlation of non-deterministic optimizers and objective levels

in the DRPTN models;

▪ Identify auxiliary problems integrated into the DRPTN models as well as the

alternative set of DRPTN models; and,

▪ Suggest improvements for DRPTN models related to overcoming the detected

challenges within the decision modeling process of DRPTN problems, paving

the way for future DRPTN research.

5.2.2 Contributions toward Meeting Objective 2

The developed methodology contributes to existing decision analysis literature by

proposing the integration of compensatory and non-compensatory decision rules, as

well as by introducing a framework for selecting decision attributes. Portraying a

systematic attribute-selection procedure as a tool, this research extracts knowledge

from the relevant literature, and systematically harnesses experts’ opinions to

produce knowledge and contribute to the construction of a better model. This

research also demonstrates how using a systematic framework influences the quality

of selected attributes in the setting of disaster recovery models. The findings further

challenge existing approaches employed for the selection of decision attributes and

argues that, to develop decision models, a formal process capable of generating

suitable decision attributes is necessary. The following list indicates contributions

and originality toward meeting Objective 2.

The presented findings, research design, and arguments in chapter three:

▪ Present the attribute selection task as a formalized discrete screening- utility

choice decision model with three sequential evaluation stages;

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▪ Introduce a prescriptive decision analysis framework integrating three

decision rules in a single decision environment for selecting attributes; and,

▪ Propose a set of evaluation criteria to evaluate both an attribute in isolation

and attributes in a set, as well as the preferential model of trade-off among

compensatory factors;

▪ Develop an integrated non-compensatory screening and compensatory choice

mathematical model as a customized value aggregation method; and,

▪ Assess the performance of the framework through surveys and interviews to

collect feedback from users on the application of the framework, performance

observation of the evaluation process, and typological analysis of the selected

set with regard to the properties of attributes.

5.2.3 Contributions toward Meeting Objective 3

The results of this study contribute to existing knowledge about concerns and values

in the reconstruction and recovery of transportation networks in the aftermath of

disasters. The recommended attribute set is the primary contribution as a result of a

delicate implementation of the framework conducted with subject-matter experts in

a critical disaster-prone context. The findings point to key factors that constitute an

set of decision attributes, and answer the question of how such an attribute set can

be identified. The results provide a practical understanding of values for drafting

post-disaster recovery plans for transportation networks. The suggested set covers

several post-disaster recovery aspects, including traffic engineering challenges,

recovery's social impact and post-disaster needs, as well as construction

management in the recovery process. It also opens a new space for developing related

measuring methods for the presented attributes in future works. The following list

indicates contributions and originality toward meeting Objective 3.

The presented findings, research design, and arguments in chapter four:

▪ Collect the DRPTN decision attributes from literature and experts;

▪ Implement the developed methodology in a real-world case study; and,

▪ Propose an improved set of attributes for Tehran DRPTN model and discuss

their applications.

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5.2.4 Application of Findings

The practical contribution of this study is to help decision-makers and analysts make

[more] informed choices and tenable decisions within the construction of DRPTN

decision models and, eventually, to develop more contextual and useful models. The

findings demonstrated in chapter two present a contextual understanding of the

process of DRPTN model construction, which provides decision-makers with insight

into what can be expected from the existing models’ performance and the limits of

these expectations. The gap analysis of DRPTN methodologies also explains what

decision-makers cannot expect to learn from a DRPTN model, as well as outlines the

uncertainties they must take into account while receiving decision recommendations

based upon an optimization-based DRPTN model.

The proposed framework presented in chapter three supports the selection of

attributes of complex decision problems or high-performance indicators of design,

policy, and engineering problems in practice. Furthermore, researchers who develop

multi-objective or multi-attribute decision models can use this framework as a guide

for the problem structuring of their modeling process. Research and practice can

apply the proposed framework for establishing a calibrated set of attributes of

decision problems even for those who are not necessarily experts in decision

analysis.

The DRPTN attribute set reported in chapter four offers DRPTN decision-makers and

modelers with a set to be utilized as decision factors for future recovery planning.

This set could also be used for evaluating existing disaster recovery plans, or as input

for the construction of DRPTN decision support systems. Additionally, future

research can use the findings of this study as a problem structuring phase when

developing new disaster recovery models. Another application of the key attributes

for disaster managers might be their use as criteria for identifying an optimized post-

disaster emergency road network in the immediate response phase. More

specifically, the integration of three attributes (link capacity, access to SP nodes, and

centrality importance) can identify disaster response routes with optimized,

involved link recovery operations, so that maximized level of service and access is

more likely.

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5.3 Future Research, Open Questions, and Remaining Gaps

Future research should recognize the significance and necessity of time and effort for

problem structuring of DRPTN decision modeling, including problem

conceptualization, executing formal processes to select decision parameters,

examining well-supported assumptions and their impacts on a model’s outcome,

assessing the typology of the decision model, and conducting sufficient

computational justification of selected methods. These tasks are particularly vital in

the field of disaster management. Academic networks and practitioners should take

the problem structuring of DRPTN as a starting point and tailor sets of attributes

according to local, context-dependent characteristics of the problem with the aid of a

systematic and transparent framework. Problem structuring should begin with

problem recognition, focusing on the discrepancy between the status quo and the

desired state of the modeled system while also accurately identifying the threshold

of uncertainties. The following sections highlight some open research questions and

knowledge gaps for future studies to approach.

5.3.1 Sensitivity to Local Minima and Converting Objectives to

Constraints in DRPTN Optimization Models

Future research is encouraged to investigate the impact of choosing deterministic or

non-deterministic optimizers on the DRPTN model's outcomes. This investigation

provides insight into the extent to which the solution DRPTN decision model is

sensitive to locally optimal solutions as compared to globally optimal ones. The

findings of this investigation support the possibility of developing an optimization

problem that is either solvable with a deterministic method or that is not completely

reliant upon global optimization. Comparing the final rank of recovery operations or

damage links in two cases where non-deterministic and exact methods are used

provides valuable knowledge regarding how the outcomes might be different which

would aid in selecting a more efficient optimizer.

Furthermore, the number of objectives, as a driving factor in choosing an optimizer,

creates a barrier in adapting deterministic algorithms. Reducing objective numbers

can decrease the computational overhead of the DRPTN optimization problem as

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long as it does not adversely impact the completeness of a model. One approach is to

define a bound or deterministic desired value for an objective, as a threshold, which

can limit the solution space and render exhaustive searches computationally more

reasonable. Some examples of this approach have been previously discussed in the

multi-objective optimization programming context. Therefore, further studies are

needed to explore this possibility and identify/quantify the desired state of post-

event network performance and answer the question of what the targeted

performance of the network is in the aftermath of the disaster.

5.3.2 Future research on the Implementation of the Framework and the

Recommended Attributes

Applying the attribute selection methodology in different contexts would provide

useful knowledge regarding the impact of local factors in the final recommended

attribute set and as auxiliary evidence for the framework's performance. Moreover,

it is recommended that future research (not only that limited to the DRPTN field)

adopt the framework in the formulation of the decision problems and implement this

formal systematic process to select attributes for their focused problems.

While the attribute set is defined, it remains a challenge to formulate a problem with

the recommended set so that it can be solved in a reasonable amount of time. The six

attributes represent four defined objectives according to the expert’s opinion and

previous disaster recovery plans described in chapter four. Since the completeness

of the attribute set is based on measuring this study-specific four objectives, it has

been shown through the concept map value tree (Fig. 4.3) in chapter four that all four

objectives have been assigned at least one indicative attribute. However, it might be

cumbersome to formulate an optimization problem that can incorporate all four

objectives and provide a feasible solution space with reasonable computational

complexity. Therefore, the attributes of the set can also be used individually if the

goal of the planning addresses one or more of the defined objectives. For example, to

focus on maximizing the efficiency of recovery planning, two attributes (travel time

improvement per unit of resources and travel time improvement per unit of recovery

time) form a representative and complete set. Therefore, future studies with different

objective sets can formulate and solve a decision problem by integrating decision

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attributes introduced in this study.

Finally, future research can investigate the possibility of reaching a complete

attribute set in the sense of addressing various multifaceted dimensions involved

with the concept of disaster risk governance. The author believes that it may be

possible to address (force-include!) various dimensions of disaster resilience

interventions, including social, economic, engineering, cultural, health, and well-

being, simultaneously in one set of attributes. However, it remains tedious (if not

impossible) to develop a decision model to operationalize this so-called “complete”

set of attributes in a computationally or cognitively manageable form for which either

a compromise or optimum solution would be feasible. Such a decision modeling with

unconceivable uncertainty is a set up for misleading decision makers who could very

likely perform better naturalistically without any decision aiding intervention. For

this reason, perhaps “the mere the merroir” is ill-advised regarding the size of the

attribute set. As a result, the third stage of the framework includes the “concise”

evaluation factor to ensure the minimized number of attributes in the set for which

its completeness— in an attainable scope of objectives— can be achieved.”

5.3.3 Does Preference for a Certain Objective Impact the Selection of

Attributes?

Although the set containing six recommended attributes is supposedly complete and

non-redundant, it is not minimized in size, which indicates the compromise in the

optimal region between size and completeness. This compromise may itself suggest

the presence of a possible indirect indication for identifying the relative importance

among the different objectives. Nevertheless, the question of understanding whether

inclination toward selecting additional attributes for an objective is derived from the

utility of the attribute or is instead derived from the preference of the objective that

the attribute measures is an intriguing question that remains unanswered. However,

one should note that it is possible that an objective demands more than one attribute

to be collectively measured.

Future research could also consider applying sensitivity analysis to understand

whether, under various point allocation scenarios, the change in preference of a

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specific evaluation factor or its assigned value could have a meaningful impact on the

rank utilities such that an indication concerning the statistical significance of certain

evaluation factor can be suggested. Additionally, sensitivity analysis is also useful for

defining the thresholds for which the change in assigned weight or values of a

particular attribute could impact the model’s outcome. In the meantime, it is

important to understand the application of sensitivity analysis, whether it can

provide meaningful knowledge or, if it does, how this knowledge can be used to

improve the decision model or reduce uncertainty.

5.3.4 Integrating Traffic Management of Surviving Networks with

Recovery Planning

The current DRPTN studies provide analytical decision recommendations for the

recovery process of a damaged network’s components after a disaster; they offer very

little in terms of how the surviving network (undamaged or slightly damaged

functional components) should be operationalized and managed to meet travel

demand in the traffic engineering context. Further research is needed to investigate

traffic management in the post-disaster surviving network; the issue of integrating

post-disaster traffic management and recovery planning remains almost untouched.

This investigation can advance our knowledge of possibilities for including traffic

management measures as choice set alternatives along with recovery projects to

maximize mobility in the network and utilize both administrative and construction

options toward satisfying the same objectives.

5.3.5 DRPTN modeling: Do Social Vulnerability Variables Matter?

Emergency and recovery planning of infrastructures against hazards in urban areas

requires addressing social factors and socially vulnerable groups while seeking to

efficiently maximize the technical objectives of the planning. It is well established that

recovery planning of transportation network, although aims at solving engineering

and construction management problem, serves the social process. The performed

content analysis reveals that social vulnerability variables have been adopted in only

12.5% of the DRPTN studies reviewed. Moreover, during the implementation of the

framework in the Tehran context, the attribute of “social vulnerability” did not

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occupy a place on the selected set, despite obtaining a relatively high utility score.

Furthermore, the observation of experts’ knowledge acquisition and review of

DRPTN literature suggests a systemic exclusion of social vulnerability indicators

from network disaster recovery planning. Future research is needed to probe the

validity of this observation and to investigate the possible causes of this exclusion.

The outcome could shed light on where social vulnerability variables lie in the DRPTN

equation.

5.3.6 Lack of Validation Tools

In the DRPTN literature review, often, the implementation of a method with

illustrative numerical examples has been interchangeably used as an alternative for

validation of a method. The fact that the DRPTN model is a complex, non-existing

decision environment explains the growing use of hypothetical, small size, and

limited numerical examples as a validation approach. Perhaps this challenge of

validation is the reason that, to date, available post-disaster recovery tools have not

meaningfully found use among decision-makers. Nevertheless, it is important to note

that a disaster recovery problem formulated for a certain scenario has limited

applicability for other similar scenarios since the network zone, phase of

reconstruction, time of disaster occurrence, damage state, vulnerability level, and

decision-makers might not remain identical for two scenarios in a real-world

instance of disasters. Therefore, scenario-based approaches should be very

conservative in generalizing the performance of the proposed model that is solely

numerically instantiated. As long as the problem under investigation is non-

observable, conducting an experiment-driven validation is a tedious task. More

importantly, this intransitivity in generalization is also valid for retrospective

validation approaches as a natural feature of non-observable problems. For example,

using historical data on traffic behavior after the 1995 earthquake in the city of Kobe

(if there is any) to validate or predict the resulting traffic behavior of a hypothetical

earthquake in the city of Tehran would not be suitable, nor could we use the observed

traffic data following that event to validate a decision model for recovery planning in

the aftermath of a hypothetical future earthquake in Kobe with a certain degree of

confidence that the second event's characteristics would mimic the behavior of the

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previous disaster and subsequent network interactions.

Accordingly, decision models for disaster recovery of infrastructures require high-

resolution comprehensive simulations of the urban system at a microscopic level that

facilitates the modeling of the performance of influential critical infrastructures and

their post-disaster interactions, as well as users’ behavior and the socioeconomic

responses of an urban system to various recovery strategies. In doing that, more

study on the collection of perishing post-event real-time data, as well as the selection,

navigation, and analysis behaviors of DMs and users, can help in developing a

simulated environment that enables to test DRPTN models as well as the findings of

this study. Developing a systematic approach to provide a degree of confidence in the

quality of non-observable models’ solutions remains a compelling direction of

inquiry for future research.

5.4 Key Recommendations for Decision-Makers and Research

The following remarks are based on thematic analysis of the current trend of DRPTN

models discussed in chapter two, the development process of decision-making model

for problem structuring presented in chapter three, and the selected attributes

suggested in chapter four. These recommendations are categorized into three groups

that address a) the necessity of the application of formal problem structuring in the

DRPTN modeling context; b) key remarks that should be considered while

developing a DRPTN decision model; and c) considerations necessary with respect to

attributes of a DRPTN model that include lessons learned from the implementation

process of the framework. Research on DRPTN, in general, has direct demand and

application in practice. While the increase in intensity and extent of disasters and

their health and socioeconomic consequences in the last two decades suggests that

the battle of risk reduction is perhaps lost for the time being, the attention of practice

recently has bounced back to “recovery planning” rebranded as “resilience”.

Therefore, the following points may also be useful for both decision-makers and

practitioners that seek to re-invest in disaster recovery planning.

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5.4.1 Problem Structuring Necessity in the DRPTN Modeling Context

5.4.1.1 Proactive structured choice rather than intuitive, reactive judgment

Many empirical studies have suggested that in low validity decision environments

where one encounters a non-observable predictive problem, even formulas

constructed simply with partial information perform equally or better than experts'

judgments based on intuition in the majority of cases (Kahneman and Klein 2009;

Meehl 1954; Kahneman 2011). Predictive intuition might be valid in decision

environments where an expert has the chance to learn and understand the stable

regularities of the system or where the system exhibits the same behavior in each

iteration of occurrence. In a random, high entropy decision environment (as is the

case in a DRPTN context), influential factors, decision players, objectives, and

decision attributes need to be identified proactively, as they are likely to be vague,

multiple, and associated with unknown or difficult-to-know uncertainties. Planning

for recovery after the occurrence of a disaster also involves factors such as

insufficient time, high stress, panic and emotional influences, unverified data, public

and media pressure, as well as a lack of tools, workforce, and the removal of the

possibility of seamless, collaborative decision-making. These challenges underscore

the necessity of problem structuring in advance for possible future DRPTN. Decision-

makers must explore, understand, and articulate their values, interests, and concerns

and accordingly establish a set of attributes through a formal process. Therefore,

context-dependent descriptive and conceptual studies are very important for

tackling non-observable problems to support problem structuring for DRPTN models

and attribute selection before a disaster occurs.

5.4.1.2 Selecting attributes through disciplined problem structuring

Disaster recovery decision problems are difficult to model; they are made only more

difficult by the fact that it is a demanding task to gain reliable insight into how

accurate or effective the models really are. This causes the disaster recovery

modeling to be more vulnerable in its problem definition and problem validation

phases. Within the process of problem structuring, determining the decision

attributes of disaster recovery planning is difficult, yet it is also the most important

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task. Selecting attributes through a structured problem framing provides

opportunities to reduce the modeling procedure's error and bias. By adopting the

proposed framework or any other formal method for problem structuring, this study

strongly suggests that decision-makers and disaster risk management planners

should employ a systematic approach toward identifying and selecting decision

attributes, indicators, and objectives. Selecting attributes and other decision factors

intuitively, arbitrarily, or without following a formalized process, in turn, increases

the likelihood of solving a partial and/or unrepresentative problem, thus committing

the error of the third kind.

5.4.1.3 Tackling the DRPTN validation challenge with problem structuring

The term "validated" might not accurately reflect on the performance and reliability

of DRPTN models, which can lead to a false impression or overestimation of the

model's capability for possible future users. I believe that validation claims should be

made with great caution in modeling non-observable problems in which predictive

accuracy is very limited. A single numerical example may neither verify nor validate

the developed model but is able to serve as a refutation cycle in testing the

performance of the model within a validation process. Nevertheless, one should note

the limitation of applying scenario-based numerical illustrative examples as the

validation phase. Earlier, this issue was illustrated more soundly by Konikow and

Bredehoeft (1992) in the ground-water modeling context. The fact that this

dissertation replicates such a recommendation from almost three decades ago is

itself alarming. Further, a comprehensive and well-stated description of validation

challenges in disaster management research is also offered by Galindo and Batta's

work (2013), in which they addressed the concept of assumption validity in the

Operations Research methods utilized in disaster operation management studies.

Therefore, it might be reasonable to assume the priority of developing error-

minimized models rather than validated ones by relying on a robust problem

structuring, including tasks such as testing the logical relationship of variables,

methodological support for identifying decision factors, justification of the selection

of solving methods, and robust verification of the preliminary assumptions and

phased outcomes, among others.

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5.4.2 Modeling a DRPTN Problem

5.4.2.1 “After disaster”: when exactly? “Disaster”: what exactly?

As a possible result of the absence of problem structuring from the DRPTN decision

modeling process, the temporal phase of planning is often neglected in the reviewed

DRPTN studies, which challenges the coherency and relevance of the planning.

Although the disaster risk management community is in the era of “biblical

confusion” (Thywissen 2006) with newly coined/adopted terms emerging in the field

such as “multi-stage”, the post-disaster planning needs to be phase specific. In both

practice and science, the “Multi-” approach is highly encouraged: multi-hazard, multi-

modal, multi-sector, multi-actor, multi-everything. However, a successful disaster

recovery plan needs to be hazard specific, sector specific, component specific, and

temporal phase specific, while taking the integrated risk assessment approach and

other sector synergies into account. The term “post-disaster” carries very little

specificity in terms of a temporal period in the aftermath of a disaster. In chapter one

(1.5.3), the distinction among different temporal phases after disasters is discussed.

DRPTN models should be tailored for a specific planning phase, such as immediate

response, mid-term recovery, or long-term. At the same time, a good DRPTN model

needs to be dynamic to expedite emergency activities in an urban area at the early

stage of the recovery phase, to establish safe and prioritized access and mobility in

the mid-term, and, later, to accelerate the recovery of the economy and social affairs.

Similarly, a DRPTN model requires a hazard-specific approach since the nature of

disruption and travel demand in the aftermath of different hazards (e.g., earthquake,

flood, or landslide) are considerably different. Therefore, local characteristics of

“disaster” should be specified as a comprehensive disaster scenario, including hazard

type, hazard intensity, hazard duration, hazard occurrence time, structural and social

vulnerabilities, and the component under study, among others.

Furthermore, during the review of DRPTN studies, I observed that the majority of

DRPTN models tended to satisfy the technical (traffic) objectives of the network,

which is mainly expressed through the performance of the transportation system

(e.g., travel time, travel cost, delay cost, network traffic flow). This means that the

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impact of recovery strategies is measured based upon their success in improving

transportation networks' technical performance, while hardly considering other

aspects of the urban system and recovery process. However, taken as a whole, civil

society, which includes entities functioning in sociocultural, health, economic, and

technical contexts, requires planning that satisfies the objective of the collective

rather than merely meeting a need of an entity.

5.4.2.2 Computational justification for the use of optimizers based on

complexity and convexity of problems

DRPTN problems require a computational justification for the selection and

application of the solving methods. Therefore, greater effort should be devoted to

identifying the mathematical problem's local characteristics with respect to both

complexity and convexity as a rationalization for choosing deterministic or non-

deterministic methods. Due to the critical context of disaster recovery, it is

reasonable to assume that DRPTN cannot afford a good-enough solution. Therefore,

when formulating an optimization-based DRPTN model, the use of a non-

deterministic method – when the problem is solvable with deterministic optimizers

that yield exact solutions – is not justifiable. Aharon Ben-tal

describes the challenge

of formulating and solving an optimization problem in the following way: “For an

optimization problem under uncertainty, the real problem is to offer models for

which the user can provide the data, and the optimizer can solve efficiently the

resulting mathematical programming problem.” An operational optimization model

recognizes the balance between complexity and convexity (i.e., aims to add features

as long as the problem results in a convex solution space). Convexity or non-

convexity can be regarded as a major criterion toward understanding the complexity

of a problem and selecting an efficient optimizer. Determining the convexity status of

a problem provides useful insight that can be used to assimilate the complexity of the

problem. The convexity analysis of a problem is superior to linearity analysis, as

proofs of convex solution space ensure the existence of a globally optimum solution,

which might not necessarily contain linear objectives or constraint functions. The

https://pubsonline.informs.org/page/moor/bental

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knowledge of complexity and convexity can be used as reliable justification for

selecting the solving algorithm.

5.4.2.3 Properties of a useful DRPTN model and a robust decision-modeling

process for DRPTN models

Several possible sets of criteria can be developed to assess the performance of post-

disaster recovery planning of transportation networks. Disaster managers can expect

that a DRPTN decision model (after the phase of emergency response) addresses the

following demands:

1) Assists the swift restoration of lifelines;

2) Provides safe mobility and an acceptable level of service in the network;

3) Ensures an adequate level of accessibility in the network;

4) Contributes to the alleviation of the calamitous social effects of disaster;

5) Functions inclusively and recognizes the socially vulnerable share of the

affected population;

6) Functions exclusively in the sense that it recognizes critical users and critical

facilities of the urban system;

7) Easy to update upon the arrival of new data; and,

8) Remains adaptable to parallel and related decisions.

Furthermore, among the many properties of a good model, a possible suggestion for

developing a DRPTN model is the following criteria:

1) Essential characteristics of the transportation system, the disaster

impact, and the recovery operation are clearly identified;

2) The decision values and objectives are collectively and clearly defined;

3) Their structure, interrelation, and hierarchy are organized;

4) Viable attributes are accurately articulated and prioritized;

5) The model is tractable, comprehensible, and optimal in size; and,

6) Data is available for its defined parameters.

It is self-evident that meeting these criteria requires structured problem

framing as a promise of a formal problem-structuring approach.

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5.4.2.4 Integrating compensatory and non-compensatory decision rules

Chapter three discusses that in some decision contexts when a number of criteria are

indefinitely more important; employing either of the compensatory or non-

compensatory decision rules alone cannot meet the characteristics of the modeled

problem. In many disaster recovery models, several aspects involved in decision

analysis are often not meaningfully compensable, judgmentally dependent, or

strongly conflicting. Hence, a compromise between values of criteria based on

compensation would not lead to a desirable choice. Integrating different decision

rules, tailored to meet the limitations of preference transition, could be a possible

solution. Incorporating both compensatory and non-compensatory decision rules in

a single decision context increases the amount of incorporated information, therefore

reducing information loss during the evaluation process. Further, when the size of an

alternative set allows, multi-stage decision environments and distributing attributes

to separated stages of the evaluation process can also increase the likelihood of

assigning more reliable weights because it is a cognitively demanding task for experts

to process information chunks related to more than five attributes (see, e.g.,

Timersman 1993; Cowan 2010). Additionally, separated decision regions based on

different decision rules, particularly in the screening decision region, would also be

an option for managing the complexity of a problem as the implementation of such a

strategy showed satisfactory performance in chapter three.

5.4.3 Attributes for a DRPTN Model

5.4.3.1 Good attributes do not necessarily form a good set of attributes

I highlighted the necessity of not only observing the properties of attributes, but

simultaneously the properties of sets of attributes, as well. This is also generalizable

to other disciplines and models that seek to represent a multi-criteria decision model.

The attribute-selection process needs to recognize the quality of a set independent

from the quality of members. Therefore, using evaluation factors for attributes in a

set is just as necessary as it is for attributes in isolation. This approach increases the

chance of achieving a complete, non-redundant, and concise attribute set.

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5.4.3.2 Accelerated temporal recovery rates contribute to network

resilience

Considering the impact of the recovery process per unit of time aims to accelerate the

resiliency of the transportation network before the network's lack of service exhausts

social tolerance. This was the argument that the experts leveled for justifying two

decision attributes of the recommended set. Therefore, adopting the attribute of

"Travel time improvement/recovery duration" facilitates capacity building for

increasing the resilience of urban areas by representing the recovery process as a

ratio of progress in restoring the technical performance of the transportation

network. Particularly, as discussed in chapter four, experts emphasized that initial

progress in the improvement of travel time (i.e., early-stage recovery) is of utmost

importance, which is also aligned with the findings of studies that quantitatively

analyze this impact and point out the necessity of attention to skew of the trajectory

of travel time progression (e.g., Zhang et al., 2017). The network recovery duration,

if used alone, is a misleading indicator for representing the success of a recovery

operation; rather, one should focus on the amount of improvement in the

performance of the system (travel time, access, etc.) or on resources consumed

within the recovery duration to represent a ratio of the recovery impact.

Additionally, "emergency routes' downtime" should also be taken as an important

factor in the emergency phase; however, this may not be the case in a network-scale

for recovery operations that occur after the emergency response phase. Once the

maximum recovery rate has been achieved, minimizing the recovery duration is of

secondary importance. Minimizing the post-disaster total recovery duration, as a

primary objective, could be arguable because the initial improvement of network

performance is crucial, which might not be entirely aligned with the rapidity of the

whole recovery process. Therefore, as two attributes of the selected set, hybrid

attributes that take into account the integration of recovery progression and

recourses/time can contribute to the network resilience.

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5.4.3.3 Centrality is a fair representative of a link's importance in terms of

accessibility

In the aftermath of a disaster, maximizing accessibility and restoring network

connectivity is of the utmost importance. However, only two studies among the 46

reviewed publications include attributes that measure the ability of a link to maintain

accessibility at a network level with regard to the geometric centrality of links.

Disregarding the topographic properties of a network to measure the accessibility

index of each link may challenge the application of models, should an alternative

attribute not be substituted. Given the uncertainty that accompanies post-disaster

traffic assignment in a perturbed network as well as a significant dearth of

information, pre-event known traffic flows might not be a reliable performance

metric for links. Therefore, it may be more reliable to determine the functional

importance of links with less reliance on traffic demand and employ flow-

independent, and connectivity-based attributes such as link capacity, lane-based

properties of links, and centrality measures.

5.4.3.4 Lifeline interaction must be considered in DRPTN, although not

necessarily as an attribute

Considering the interaction of transport network components with other critical

infrastructures is a relevant factor for prioritizing the recovery of links for early-stage

assessment and damage control in other linear interconnected infrastructures such

as electrical grids and gas-delivery systems. Timely attendance to other damaged

lifelines is essential to avoid secondary, technical, and cascading hazards. However,

this attribute was not included within the selected set in this study, as it fails to meet

the condition of discriminability. The reason for this exclusion was that DMs argued

that almost all major links in Tehran’s road network have overlap with at least one

lifeline, such as a natural gas network or water-delivery system, that prevents a

meaningful comparison among links based on such an overlap. However, DMs

advised that this attribute should be treated as a decision constraint, included in

protocols at the operational and tactical levels in which cascading or technological

hazards are predicted or considered in critical nodes clusters under the category of

accessibility.

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174

5.4.3.5 Understandability and certainty are incentive factors for the

favorability of attributes

Based on the values that experts assigned to the attributes of the alternative pool in

the choice region, the evaluation factors of “certainty” and “understandability”

supplied more information than “directness” and “representativeness.” The entropy

value of certainty and understandability suggests that experts were more sensitive

to these factors while evaluating the attributes since the assigned values were more

diverse for “certainty” and “understandability” and more uniform for “directness”

and “representativeness” factors. This can also suggest that for the DMs who used

this framework, “certainty” and “understandability” of an attribute have higher

relative importance than two other evaluation factors. Therefore, in that context, a

certain and non-ambiguous disaster recovery planning, although not necessarily

optimal, was preferred; i.e., a more understandable and certain DRPTN attribute

could compensate for its lower representativeness and directness. Similarly,

sensitivity analysis presented in chapter four also points out the relatively higher

sensitivity of the outranked attributes to the weight of the “certainty” evaluation

factor, while this sensitivity was significantly less for “representativeness,” for

instance. The inherent uncertainty in the DRPTN context leaves less room for adding

uncertainty to the DRPTN model by including attributes that introduce uncertain

values, either due to limitations of measurement, data, or ambiguous definitions.

5.4.3.6 For future use of the framework

For the further use of this framework, it would be advantageous for a moderator to

oversee the evaluation session and act as an opposing voice, if necessary, to facilitate

the extraction of DMs’ knowledge. However, there is an indirect association between

the degree of control and subjectivity within moderating this framework. The

principal task is to find a fair trade-off and keep this compromise balanced and

understand where this control leads to creativity and/or hinders it. Furthermore,

when using the proposed framework, one must take into account the size and

completeness of the alternative set. A so-called diverse complete set of alternatives

is required since the result will be as complete as the alternative pool. Nevertheless,

analysts and future users of the framework must establish a desired trade-off

Disaster Recovery Planning of Transportation Networks; Problem structuring and decision attributes

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between the desired completeness and the complexity of the model. Users of the

proposed framework can also consider reducing the initial alternative pool's size by

allowing homogenous attributes to merge into a single one and proceed with the

resulting attributes in a smaller alternative pool. Finally, when choosing a method of

aggregation, I suggest noting the tractability of calculations, as well as minimized

processing of the experts' numerical input.

5.5 The Art of Modeling in Disaster resilience planning Contexts

There are infinite ways to model a problem. Determining “how good the model is”

appears to be as difficult as indicating otherwise. At the same time, the urge to

present “innovative research” and “novel contributions” may drive researchers to

include sets of attributes distinct from those that have already been introduced in the

literature. This impulse encourages the intuitive selection of attributes on the sole

merit of “having not been previously addressed.” Perhaps for the same reason, some

journals and communities express concerns about research designs with artificial,

unsupported variables and arbitrarily selected attributes (e.g., “4OR; A Quarterly

Journal of Operations Research”). The reason for this concern is that the same process

can indefinitely be repeated with different decision parameters (typically formulated

into a complex NP problem and solved with a randomly chosen optimizer) without

providing meaningful insight into the problem under investigation.

The demand is rising for numerically analytical automated studies that are conducted

with so-called sophisticated and novel combinatorial meta-heuristic algorithms and

visualized with cutting-edge tools and codes. However, the method-rich but

methodology-poor syndrome in chapter two, indicates that for sensitive, critical, and

low-validity decision environment problems such as those in disaster management,

the level of effort should also be proportionally channeled to initially build up

descriptive, conceptual, and contextual foundations of the problem to support and

justify the methods used and methodologies employed. This could open up

opportunities to develop simple, representative, robust, and understandable models.

Non-conformist critical, independent research is needed to question commonly held

assumptions and to select tools and methods that are context-appropriate and serve

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the decision problem. The field of DRPTN needs a dedicated, strong problem-

structuring phase to avoid tailoring the problem to the method at hand, rather than

to either find or develop a tool that submits to the property of the problem under

consideration.

The goal for decision modeling in disaster recovery planning should focus on the

exclusive and tractable format of the model. The author is aware that, in decision

analysis, exclusivity and tractability often conflict. Nevertheless, harnessing the

advantages of problem structuring allows for greater attention to the contextual and

local situation/information of each problem and avoids one-method-fits-all

formulations. This approach supports the necessity of context-dependent features of

disaster recovery models and helps modelers prioritize and include what is most

relevant and important for each specific problem.

Many experienced researchers refer to problem structuring, in general, as an art. In

the DRPTN context, regularity is rare, data is often absent, and DMs' experience is low

because they do not have many chances to familiarize themselves with regularities

of the problem and decision environment. These properties are attributes of the

stochastic nature of disasters, the infrequent and sudden-onset occurrence of major

hazards, various unknowns and hardly predictable variables, and chaotic post-

disaster conditions. Therefore, to compensate for these inherent challenges of

DRPTN modeling, problem structuring in this context might require more than just

art to measure up to the task at hand. One approach is to minimize bias and error in

the modeling and solving process by ensuring that the decision model's components

are generated through a formal, systematic process that can be, to a large extent,

obtained by following a methodological problem-structuring approach.

Furthermore, in the era of real-time big data and computational power, the art of

modeling turns out to be a “complexity manipulation,” that is to say, to find a balance

between the amount of complexity we are willing to transmit into our model against

the amount of uncertainty we add to the model in return. In the problem structuring

of optimized DRPTN decision models, modelers should decide whether they prefer a

less accurate solution to a loosely perceived problem that fairly reflects the

complexity of the system or a more accurate solution to a well-perceived problem

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177

that does not completely represent the complexity of the modeled problem.

According to the argument leveled in chapter two, for DRPTN models, the complexity

of the problem in terms of comprehensiveness of decision parameters is directly

associated with the uncertainty of results. Therefore, I argue that one feature of a

well-perceived modeled problem is that the modeler considers the limitation and

uncertainties of the modeling procedure and identifies the minimum essential

characteristics of the system with which the directness and completeness of the

decision model can be maximized. In other words, it is important that the possible

sources of errors and uncertainty be minimized by confining decision parameters to

those that cover the most important concerns about the defined objectives and that

possess the desired properties of a good attribute. Well-perceived problems result in

a tractable model, in which the major relevant decision parameters and information

are isolated, prioritized, and organized to allow for accurate and efficient answers or

a close approximation to the mathematically programmed model.

To address these concerns, methodological problem structuring can assist modelers

in an accurate perception of the problem and its modeling process. A successful

disaster resilience decision model calls for formal problem structuring to support the

design of a model with a well-adjusted relationship between the perception of a

system and the complexity of its model. The model should be capable of being solved

at a reasonable computational cost and return deterministic solutions or proof as to

how the returned solution relates to the ideal solution. Even though DRPTN decision

models are complete, novel, and original in automation, visualization, and

mathematical programming, without strong problem structuring, they remain

incomplete and constitute partial, poor reflections of the system's collectivity, failing

to grasp adequate, logical relationships among the components of the modeled

systems.

Developing a useful model (if there is such a thing) requires dedicating

significant and serious efforts to creative, disciplined problem structuring while

accepting as little compromise as possible with regard to the completeness and

representatives of a model. The art of modeling in disaster recovery contexts relies

upon the extent of effort dedicated to the model's problem structuring.

“As they can never reflect the whole, they fail in that they are partial” (Bos and Tarnai, 1999).

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178

5.6 References

1. Bos, W., Tarnai, C., 1999. Content analysis in empirical social research.

International Journal of Educational Research, 31(8), 659–671.

2. Corner, J., Buchanan, J., Henig, M., 2001. Dynamic decision problem structuring.

J. Multi‐Crit. Decis. Anal., 10: 129-141. doi:10.1002/mcda.295

3. Cowan, N., 2010. The Magical Mystery Four: How is Working Memory Capacity

Limited, and Why?”. Current directions in psychological science, 19(1), 51–57.

https://doi.org/10.1177/0963721409359277

4. Galindo, G., Batta, R., 2013. Review of recent developments in OR/MS research

in disaster operations management. European J. of Operational Research,

230(2), 201–211.

5. Kahneman, D., 2011. Thinking, fast and slow. New York, NY: Farrar, Straus and

Giroux.

6. Kahneman, D., Klein, G., 2009. Conditions for intuitive expertise: A failure to

disagree. American Psychologist, 80, 237–251.

7. Keeney, R., 2007. Developing objectives and attributes. In: Edwards, w., Miles,

r., f. & von Winterfeldt, d. (eds.) Advances in Decision Analysis. New York:

Cambridge University Press.

8. Konikow, L.F., Bredehoeft, J.D., 1992. Groundwater models cannot be

validated? Adv. Water Resourc., 15, 75-83.

9. Meehl, P.E., 1954. Clinical versus statistical prediction: A theoretical analysis

and a review of the evidence. Minneapolis, MN: University of Minnesota Press.

10. Thywissen, K., 2006. Components of risk: a comparative glossary. United

Nations University Institute for Environment and Human Security. Bonn,

Germany.

11. Timmermans, D., 1993. The impact of task complexity on information use in

multi‐attribute decision making. Journal of Behavioral Decision Making, 6, 95-

111.

12. Zhang, W., Wang, N., Nicholson, C., 2017. Resilience-based post-disaster

recovery strategies for road-bridge networks. Structure and Infrastructure

Engineering, DOI: 10.1080/15732479.2016.1271813

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Appendix

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Appendix A

(Examples of information for disaster scenario familiarization)

Table A.1: Example of information presented to experts for familiarity with the context

and disaster scenario

City

Tehran

Region code

Zone numbers

Area

4690 Hectare

Population

Approx. 1.000.000

Households

256992

Population density

144 p/h

Perimeter

40584

Hazard(s)

Earthquake, secondary hazards

Season

Spring

Network status

Damaged links approximately 60% of network in slight, medium and

sever damages levels, 50% of the network nonoperational

Operational status

Main phase of search and rescue and emergency response is

accomplished

Available data

Demographic, damage level, geometric, service providing sites,

topology, traffic counts, available resource, travel times, critical nodes,

…

Temporal phase

Mid-term recovery after emergency response (72 hours)

Disaster Recovery Planning of Transportation Networks; Problem structuring and decision attributes

181

Figure A.1: A screenshot of a material example used to familiarize experts with the case

study concerning data available for post-disaster recovery planning

Appendix

182

Appendix B

Table B-1: Rank and utility of 33 attributes of choice region

Rank

Attribute

Utility

Access level of link to SP nodes

29.67575758

Travel time improvement/resources

29.37575758

Travel delay of link *flow of the link

28.91212121

Duration* travel time improvement

28.44848485

Centrality importance 

27.94242424

East-west and north-south connectivity

26.63030303

Impact on total network travel time

26.3030303

Link Capacity

25.87878788

Connectivity to other traffic zone

25.52424242

Topography

24.17878788

Social vulnerability*link delay

23.548

AAWT

23.25757576

Social vulnerability* zone travel demand

22.948

AADT

22.15151515

Link Density

22.02424242

Disaster Recovery Planning of Transportation Networks; Problem structuring and decision attributes

183

Recovery efficiency

21.96969

Total network Traffic flow

21.2

Impact on Total network flow

20.77272727

Total Network Travel time

20.54848485

Level of service

20.24242424

Population*link delay

20.14848

Travel delay imposed by link failure

20.05151515

Links to airport and exit ways

19.2969697

Population density based on age, gender and number of households

18.71818182

Traffic redundancy

18.67575758

Access to socially important sites

18.25151515

Social importance

18.06060606

Travel demand

17.29393939

Recovery duration of link

17.01818182

Link volume

16.06666667

Relief demand nodes

15.3969697

Population accessed by the link

15.33636364

Depot and need nodes

14.22424242