Parsimonious AHP-DEA integrated approach for efficiency evaluation of production processes

Ammirato, Salvatore; Fattoruso, Gerarda; Violi, Antonio Article Parsimonious AHP-DEA integrated approach for efficiency evaluation of production processes Journal of Risk and Financial Management Provided in Cooperation with: MDPI – Multidisciplinary Digital Publishing Institute, Basel Suggested Citation: Ammirato, Salvatore; Fattoruso, Gerarda; Violi, Antonio (2022) : Parsimonious AHP-DEA integrated approach for efficiency evaluation of production processes, Journal of Risk and Financial Management, ISSN 1911-8074, MDPI, Basel, Vol. 15, Iss. 7, pp. 1-15, https://doi.org/10.3390/jrfm15070293 This Version is available at: https://hdl.handle.net/10419/274815 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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Journal of Risk and Financial Management 15: 293. https:// doi.org/10.3390/jrfm15070293 Academic Editor: Thanasis Stengos Received: 1 June 2022 Accepted: 29 June 2022 Published: 30 June 2022 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Copyright: © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). Journal of Risk and Financial Management Article Parsimonious AHP-DEA Integrated Approach for Efficiency Evaluation of Production Processes Salvatore Ammirato 1,* , Gerarda Fattoruso 2and Antonio Violi 2 1 Department of Mechanical, Energy and Management Engineering, University of Calabria, 87036 Rende, Italy 2Department of Law, Economics, Management and Quantitative Methods, University of Sannio, 82100 Benevento, Italy; [email protected] (G.F.); [email protected] (A.V.) *Correspondence: salvator[email protected] Abstract: This document proposes an innovative composite indicator to measure and control the performance of production processes. The aim is to provide a tool for controlling the efficiency of the processes, assessed in relation to the number and the impact of occurring “errors”, which can take into account the opinion of experts in the specific domain. This allows for the definition of a more realistic and effective decision support system. Our composite indicator is based on an integrated approach based on Data Envelopment Analysis (DEA), and a new multi-criteria method such as Parsimonious Analytical Hierarchy Process (PAHP). The results obtained on a real test case, based on the automotive production domain, show that the composite indicator built with PAHP-DEA allows us to have clear evidence of the efficiency level of each process and the overall impact of errors on all the processes under evaluation. From a methodological point of view, we have for the first time combined the new thrifty AHP with the DEA. From an application point of view, this work introduces a new tool capable of evaluating the efficiency of production processes in an extremely competitive sector, exploiting the knowledge of the experts in the domain of errors, internal processes and the dynamics that occur. Keywords: DEA; parsimonious AHP; composite indicator; MCDA; processes efficiency 1. Introduction The production processes represent the fulcrum for achieving the efficiency objectives set by the companies (Vesperi et al. 2021). The automotive sector represents a particularly complex and dynamic application field (Canonico et al. 2021) and the companies operating in this sector have a particular attention to the analysis of internal production processes in terms of technical efficiency (Fattoruso et al. 2022). The modifications of plants and working methods, the optimization of procedures in order to reduce / eliminate waste and losses, process flexibility and customer satisfaction with the final product represent some of the cornerstones of the success in the automotive sector (Schonberger 2010). Downstream of a production activity, the analysis of the efficiency of the processes is determined in relation to the number of errors, or discrepancies on the products, that occur in them: (a) if the output is satisfactory, the process must be standardized and maintained; (b) if the output is not satisfactory, it will be necessary to analyze the causes that generated the errors and implement countermeasures within the process to prevent them from recurring (Petrillo et al. 2019). It therefore becomes necessary for companies to adopt approaches that aim at efficiency in terms of improving production processes through the logic of optimization, monitoring and integration of systems and work methods; one of the approaches that meets these needs is Business Process Management (BPM) (Ammirato et al. 2019a). A BPM approach can be useful to ameliorate production processes since it follows the process life-cycle by defining feasibility analysis necessary to avoid wasting time and resources, supporting managers in controlling that it is done in the best possible way and J. Risk Financial Manag. 2022,15, 293. https://doi.org/10.3390/jrfm15070293 https://www.mdpi.com/journal/jrfm J. Risk Financial Manag. 2022,15, 293 2 of 15 verifying how well the results are aligned with the stated prevailing objectives, favoring corrective actions. A BPM approach in this sense means responding to the need to be quick in the implementation of new solutions so as not to affect daily operations. This goes through constant monitoring and refinement of processes to strengthen their capacity and repeatability. Therefore, it is necessary to lay the foundations for the definition of an efficiency process and maintaining and improving the process itself over time. Many authors point out that the effects and innovation of a BPM approach within business processes are highly amplifying through the use of Internet-based (IT-based) technologies, particularly from Internet of Things (IoT) technologies (see, e.g., Van der Aalst 2013; Gubbi et al. 2013 ; Ozil 2015 ). Innovation due to the fact that IoT-type technologies transform workplaces into cyber-physical spaces (so-called “smart environments”, see Laput et al. 2017) thanks to the simultaneous introduction of smart objects, cloud computing, big data and artificial intelligence (Monostori 2014). Adoption of IoT technologies requires the definition of effective innovation management, more complex than a simple automation process (Forrester 2015). Indeed, IoT makes it possible to integrate people and automated systems into the process through structured workflows to achieve better performance (Del Giudice 2016). The analysis of efficiency in production processes therefore passes through a careful analysis of the data relating to the errors that occur in them (Hafizi et al. 2019). The IoT devices collect large amounts of data that are processed, transmitted, managed and tracked. Without the ability to make this data usable and to create knowledge, there is no innovation (Eftekhari and Akhavan 2013). In order to allow IoT technologies to be integrated and managed in the best possible way in companies to improve the efficiency of processes, a method is required that allows for identifying the way in which data must be selected and processed (Ammirato et al. 2019b). The research questions that guided this work are as follows: • Is it possible to introduce an efficiency indicator in companies in the automotive sector that helps decision makers to pursue efficiency objectives? If yes, is it possible to integrate this indicator adopting IoT technologies through a BPM approach? • Is it possible to define an indicator that provides the involvement of decision makers? If yes, does the involvement of the decision maker in the construction of efficiency indicators provide reliable results? Our goal is to propose a methodological approach that provides a new indicator for controlling the efficiency of processes and that takes into account the opinion of the domain experts. In this sense, the goal is to have a more realistic and effective decision support for the company. We report our theoretical background in Section 2, methodological approach in Section 3 , while in Section 4we illustrate a case study and discuss the main results. In Section 5we report some concluding remarks. 2. Theoretical background From the literature emerges that an effective tool for monitoring and measuring performance and its efficiency are the Composite Indicators (CIs) (Esty et al. 2006). These indexes are defined through the weighting and aggregation of sub-indicators (Saisana et al. 2005), representing critical aspects in the application domain under consideration. The use of CIs allows the overall information of the sub-indicators to be represented—even when they are controversial—in a comprehensive way. Among the most used methodologies for the construction of composite indicators are the Multi-Criteria Decision Aiding (MCDA) (cfr. e.g., Munda 2005;Zhou et al. 2006;Hajkowicz 2006) and Data Envelopment Analysis (DEA) (cfr e.g., Cherchye et al. 2007;Ulucan and Atıcı 2010). A common feature of MCDA approaches is the determination of weights with the involvement of Decision Makers (DMs). This aspect is very often criticized as the objectivity of weights is discussed (Wang 2015). Instead, the non-parametric DEA approach defines weights endogenous for all Decision-Making Units (DMUs) not providing any prior J. Risk Financial Manag. 2022,15, 293 3 of 15 information (Cherchye et al. 2008). In this sense, the problem of the objectivity of weights is solved (de Almeida and Dias 2012). In the construction of a composite index, the DEA framework provides two main approaches: definition of common weights or differentiated weights for all DMUs. The identification of common weights requires that all DMUs have the same set of weights (see e.g., Emerson et al. 2012): the logic is that the weights should be fair and consistent for each DMU (Hatefi and Torabi 2010) in order to have an objective comparison. The determination of the weights in a differentiated way for the DMU involves the use of a system of preferences that allows maximizing individual performances (Zhou et al. 2007,2010). Several authors integrate the use of DEA with MCDA methods (cf., e.g., Olanrewaju et al. 2013;Shakouri et al. 2014;Gouveia et al. 2021;Wang and Dang 2021;Rivero Gutiérrez et al. 2022;Antonio et al. 2022) by exploiting their similarities in formulation (Stewart 1996). Hatefi and Torabi (2010), e.g., propose the construction of a CI through an MCDA-DEA approach in which the entities are evaluated through a series of common weights. The authors propose a comparative study between the models present in the literature. Wang (2015) also defines a CI by defining weights with MCDA approaches. The author also proposes the study of the indicator in the evolution over time by analyzing the underlying driving factors. Many authors, in particular, foresee the integration of DEA with Analitic Hierarchy Process (AHP) highlighting its advantages. Azadeh et al. (2008) present a method for the performance improvement and optimization of railway systems through simulations involving an integrated DEA-AHP approach. The authors highlight that the integration between DEA and multicriteria approaches is particularly useful when both quantitative and qualitative variables are present. Lin et al. (2011), again, in their work in which they integrate DEA-AHP for the performance evaluation of Chinese local governments, highlight the usefulness of the simultaneous use of DEA with MCDA methodologies when the problem is characterized by several criteria and one wants to evaluate and classify several alternatives. For further work that propose DEA-AHP integration underlining its advantages, one can consult Kuo et al. (2010), who used the DEA and Fuzzy AHP integrated approach for supplier selection by presenting a case study on an auto lighting system company, and Wang et al. (2022), who use DEA and Grey AHP for the analysis of adequacy policies and support mechanisms for sustainable solar energy. It appears evident that the use of MCDA with DEA approaches are particularly useful for systems in which there are qualitative and quantitative evaluation measures, such as in production systems in our case. From the analysis of the literature, it can be seen that among the multicriteria methods most used in the integration with DEA approaches is the AHP method. The AHP method is a widely used method in multi-criterion decision contexts (Ishizaka et al. 2011). We recall that the AHP is based on the construction of pairwise comparison matrices (PCMs) of alternatives and criteria in order to obtain the priority of the elements being evaluated (Cavallo and D’Apuzzo 2009). However, it should be noted that the literature on MCDA highlights the limitations of AHP for addressing complex decision-making problems. Among the most relevant problems are the number of alternatives which must not be greater than 7 (Ishizaka and Labib 2009) and rank inversion (Belton and Gear 1983), problems in which the addition or deletion of one or more alternatives can modify the final rank (to deepen the debate in the literature, see Maleki and Zahir 2013 and Krejˇcíand Stoklasa 2018 ). Taking into account the advantages of integrated approaches of AHP and DEA and evaluating the limits that the AHP presents in complex problems, our work proposes for the first time the use of a new version of the AHP, the Parsimonious AHP (PAHP), with DEA. PAHP, proposed in the literature in 2018 (Abastante et al. 2018), has all the advantages of the classic AHP and solves its problems thanks to the introduction of reference points that allow the decision maker to: - analyze problems with a very large number of alternatives; - considerably reduce the number of pairwise comparisons; - make the decision-maker more aware in defining their preferences; J. Risk Financial Manag. 2022,15, 293 4 of 15 - solve rank reversal problems. To learn more, see (Abastante et al. 2019). Therefore, the aim of this paper is to define an innovative approach, based on the integration of PAHP and DEA methodologies, for the efficiency evaluation, by means of the measurement of a proper CI. The proposed framework is also compared in terms of decision support provided, for evaluating the efficiency of production processes. In line with the principles of IoT technologies adoption by means of a BPM approach, the proposed framework can serve as a base for an automated tool able to effectively monitor and control production processes in manufacturing. The mathematical model for the calculation of CI requires the availability of data relating to a certain set of errors, which in this context act as sub-indicators of performance, which occurred in a given time interval within a certain homogeneous set of processes. Therefore, the aim is to determine for each process, seen in this context as a Decision- Making Unit, a performance measure constructed in terms of a CI, i.e., a complex indicator obtained as a weighted average of various sub-indicators. In this type of analysis, the crucial aspect consists of determining the weights to be associated with the individual sub-indicators in evaluating the performance of each process. In order to ensure objectivity in the comparative assessment process, common weights will be adopted in determining the efficiency of each DMU, and the results will be compared with those obtained with classical Data Envelopment Analysis approaches. As already stated, the approach we are proposing can be considered as a subjective approach: the weights are defined through an evaluation procedure of the sub-indicators according to a series of criteria suggested and validated by the decision-makers. Classical objective approaches, on the contrary, determine the weights to be associated with each sub-indicator (error) in a completely automatic way, by solving one or more of the optimization models. We propose a classification of the performance of DMUs, with very recent approaches of multi-criterion analysis, analyzing their potential for improvement by carrying out both static and dynamic analyzes. The innovative elements of this work are the definition of a composite indicator through the integration of a very recent multicriteria method such as the PAHP with the DEA. Furthermore, our approach provides for the active involvement of DMs as the major holders of knowledge on company managerial issues, essential for being able to interpret and fix errors that occur in the company. In this way, we try to give a healthy subjectivity that can give more coherent solutions in this context than the classic DEA approaches. Moreover, the mathematical models and methods that we propose can be easily implemented and act as the kernel of a decision support system, capable of interfacing with current information tools and with the IoT technologies in use in the production plant. This enables an effective innovation management by combining people and automated systems to achieve better performance. 3. Materials and Methods The method we propose aims at evaluating the performance of a set of (production) processes M , in terms of occurrence and impact of a set of errors E . According to the DEA framework, processes can be considered the DMUs under evaluation, assumed to have one dummy input with unitary value (see, Hatefi and Torabi 2010), while errors are the (undesirable) outputs. The overall efficiency of process s is measured by means of a CI obtained starting from the weighted sum of the frequency of each error ioccurring in s(eis): CIs=1−"∑ i∈E wieis#NORM (1) J. Risk Financial Manag. 2022,15, 293 5 of 15 In order to compare the CIs obtained for several processes, even very different, we have normalized the value of the weighted sum by considering the ratio with the maximum value measured within the process set, so to have for each process a value in the [ 0.1 ] range. For the evaluation of the relevance of each error, we consider a set of criteria G , where gj(ei) define the evaluation of the error ei with respect to criterion gj . We denote with eis the occurrence of error i on process s . The determination of the weights for each error wi , common for all the processes, represents a weighted sum of the criteria priority pj and the errors local priority lpi: wi= j ∑ j=1 lpi·pj(2) where: pjis determinated as follow: A·v=λmax·v(3) In formula (3) A is the Pairwise Comparison Matrix (PCM) (see e.g., Cavallo and D’Apuzzo 2009;Cavallo and Brunelli 2018) built through a judgment of comparison ( eij ) between ordered pairs of errors ( ei , ej ) by the DM, using the Saaty Scale (Saaty 1977). A is a matrix: (a) Anxn positive; (b) reciprocal if eij =1 eji ∀i , j and with eii =1∀i ; (c) made up of finite elements, in fact for each criterion gj,eij 6=∞∀i,j(Greco et al. 2016). Moreover, v is the priorities vector v=v1, . . . , vi, . . . , vj, . . . , vn (see e.g., D’Apuzzo et al. 2007). Considering that the dominance coefficient of each pair of errors eij =vi vj is a ratio of their respective weights, is verified that A·v=n·v. In fact:     v1 v1. . . v1 vn . . ..... . . vn v1. . . vn vnj       v1 . . . vn   =n   v1 . . . vn    For the algebra of the matrices v it turns out to be an eigenvector for the matrix A with eigenvalue n . Considering that {λ1, . . . , λn} are n eigenvalue of A , with Anxn = eij , if eij =1 ∀i=j so n ∑ i=1 λi=n , principal eigenvalue λmax =n . At this point, it will be sufficient to calculate the vector that satisfies the equation (3). That is, it will be sufficient to determine the principal eigenvector associated with the eigenvalue λmax of the matrix A and subsequently normalize von the sum of its elements (Saaty 2003;Ishizaka and Nemery 2013). lpiis obtained with a linear interpolation: lpi=hlj+hlj+1−hlj lj+1−lj ·(rj(ei)−lj(4) in which: lj represents a reference point that allows us to reduce the pairwise comparison (Abastante et al. 2019) between the errors. We consider as reference points the same points that partition the data interval by equal parts (Abastante et al. 2018); hlj is the priority associated to reference point lj obtained with the eigenvalue method (formula (3)); rj(ei)represents the evaluation of the error eiwith respect to criterion gj; hlj+1−hljdeterminate the weighted difference between two reference points; lj+1−ljrepresents the difference between two reference points. We highlight that pj is defined by means of the PCM built with verbal evaluation by DMs using Saaty Scale (Saaty 1977); instead, lpi is determinated with a linear interpolation formula, this allows to compare the real performance of the errors rj(ei) respect the value of reference points ljdefined with the PCMs. J. Risk Financial Manag. 2022,15, 293 6 of 15 4. Results 4.1. Description of Case Study Our testing experience has been carried out in an international company operating in the automotive sector. The plant under analysis is located in southern Italy and carries out the assembly of the components on the engines. The production process of the plant is characterized by 9 processes: −Process 1: distribution shaft; −Process 2: cast iron; −Process 3: base crankshaft; −Process 4: base all; −Process 5: cylinder head; −Process 6: short block; −Process 7: cylinder head assembly; −Process 8: long block; −Process 9: picking. In each process, operations are performed on the engine before it moves on to the next process. The main objective of the company is to guarantee the efficiency of the processes by reducing the errors that occur in the plant. The processes considered are impacted by 19 main errors categories; by way of example, a category of error can be considered a tightening operation (for reasons of confidentiality, the names of the other categories of errors are not reported). Each error can occur in one process or in multiple processes. The data are systematically collected in matrices by the company as errors occur in each process. We analyzed the errors related to the 9 processes that occur in two consecutive years. Table 1shows the data relating to the frequency of each Category of Error (EC) for each process considered for the 2019 and for 2020. Table 1. Errors found in processes in 2019 and 2020. 2019 2020 Process 1 Process 2 Process 3 Process 4 Process 5 Process 6 Process 7 Process 8 Process 9 Process 1 Process 2 Process 3 Process 4 Process 5 Process 6 Process 7 Process 8 Process 9 EC 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 EC 2 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 4 0 0 EC 3 0 0 0 0 3 0 0 0 0 0 0 0 0 0 1 0 0 0 EC 4 0 0 0 0 0 0 66 0 0 0 0 0 0 0 0 1 0 0 EC 5 0 0 0 0 0 0 2 0 0 0 0 0 0 27 0 0 0 0 EC 6 0 0 0 0 2 0 2 0 0 0 0 0 0 0 0 4 0 0 EC 7 0 0 1 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 EC 8 6 0 0 4 0 0 22 0 0 134 0 0 0 5 17 0 0 350 EC 9 0 7 0 0 0 0 0 0 0 0 0 0 0 0 35 34 30 0 EC 10 0 0 0 0 0 2 0 0 5 0 0 0 0 0 0 4 0 0 EC 11 38 0 0 0 0 0 0 2 0 22 0 0 0 1 0 18 0 15 EC 12 0 0 0 0 0 0 7 0 2 0 0 0 0 0 0 1 2 0 EC 13 0 0 0 0 0 0 11 0 0 0 0 0 0 0 0 1 0 1 EC 14 0 0 0 0 0 1 0 0 0 0 0 0 0 0 3 0 0 0 EC 15 0 0 0 0 2 1 0 0 0 0 0 0 6 0 0 4 0 0 EC 16 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 2 EC 17 0 0 3 1 5 0 14 0 0 0 0 3 0 0 0 70 100 3 EC 18 1 0 0 0 0 0 11 0 0 0 0 0 0 0 0 3 42 0 EC 19 0 5 0 0 0 0 0 11 0 0 10 0 0 0 0 0 0 0 TOTAL 45 12 4 5 12 6 137 13 7 156 10 4 6 33 56 145 174 371 J. Risk Financial Manag. 2022,15, 293 7 of 15 In complex realities such as the automotive production plants, the knowledge of the decision maker on business problems is essential to be able to interpret and correct the errors that occur in the company; when talking about the efficiency of production processes means not only reducing errors but also knowing and evaluating them individually so that they can be faced and prevented from repeating themselves. Upon detecting any errors in the processes, the company provides for their evaluation taking into account four criteria: frequency, cost, detection and severity. It should be noted that the criteria are identified and normally used by the company for the evaluation of errors. In this sense, we can assume they are suitable for the adoption within our approach. Error evaluation aims to define a priority for each error. This allows us to analyze the efficiency, also taking into account the type of error that occurs in it (see, Fattoruso et al. 2022 ). On the basis of these evaluations, we have built a procedure for the weights definition with an PAHP approach which foresees the direct involvement of the decision maker. In our case study it was built with the involvement of the control manager on the production process that from here on we will call DM for simplicity. The control manager has the task of verifying the correct functioning of each process and of detecting, analyzing and defining corrective actions for the errors that occur in it. 4.2. Solution Analysis In order to calculate the weights wi for each error we have applied the methodology described in Section 2. The first step is the determination of the criteria priority pj . For this purpose, we have built with the DM a PCM (Table 2), obtaining the priority vector by applying formula (3). For the construction of the PCM shown in Table 2, we asked the DM to compare the criteria in pairs, expressing his preferences, using the Saaty scale (Saaty 2001). Table 2. Pairwise comparison matrix between criteria. Frequency Cost Detection Severity pj Frequency 1 1/2 1/5 1/9 0.046 Cost 2 1 1/3 1/9 0.076 Detection 5 3 1 1/9 0.143 Severity 9 9 9 1 0.736 Consistency Index 0.09 The second step for the construction of wi is the identification of errors local priority lpi . The evaluation rj(ei) has been provided by the company (we report the evaluations in Table A1 in Appendix A). Based on the number of errors to be analyzed as suggested by Abastante et al. (2019) we have identified 6 reference points ( lj ) (Table A2 in Appendix A) and we built the PCMs for each considered criterion by deriving the priority hlj (we show the priorities hlj in Table A3 in Appendix A) with formula (3). Thus, applying formula (4) we derived errors in local priority showed in Table 3. In Table 4we report the weight wi obtained with formula (2). J. Risk Financial Manag. 2022,15, 293 8 of 15 Table 3. Errors local priority for 2019 and 2020. 2019 2020 Frequency Cost Detection Severity Frequency Cost Detection Severity EC 1 0.034 0.382 0.163 0.382 0.032 0.382 0.134 0.118 EC 2 0.036 0.382 0.163 0.382 0.033 0.382 0.222 0.382 EC 3 0.037 0.382 0.163 0.250 0.032 0.382 0.222 0.250 EC 4 0.391 0.057 0.385 0.250 0.308 0.113 0.385 0.340 EC 5 0.036 0.083 0.134 0.382 0.038 0.194 0.086 0.014 EC 6 0.039 0.083 0.385 0.250 0.033 0.194 0.031 0.118 EC 7 0.036 0.083 0.134 0.250 0.032 0.194 0.134 0.250 EC 8 0.129 0.083 0.134 0.250 0.312 0.157 0.222 0.250 EC 9 0.045 0.057 0.134 0.382 0.055 0.113 0.092 0.118 EC 10 0.045 0.057 0.134 0.250 0.033 0.113 0.134 0.118 EC 11 0.172 0.057 0.075 0.160 0.028 0.113 0.177 0.160 EC 12 0.048 0.057 0.075 0.250 0.033 0.113 0.046 0.250 EC 13 0.052 0.057 0.075 0.250 0.032 0.113 0.395 0.382 EC 14 0.034 0.057 0.075 0.382 0.033 0.113 0.177 0.118 EC 15 0.037 0.057 0.075 0.250 0.034 0.113 0.177 0.250 EC 16 0.034 0.057 0.075 0.250 0.032 0.113 0.177 0.118 EC 17 0.088 0.057 0.075 0.160 0.088 0.113 0.177 0.278 EC 18 0.054 0.057 0.075 0.160 0.043 0.113 0.177 0.278 EC 19 0.065 0.057 0.385 0.250 0.017 0.113 0.385 0.382 Table 4. Errors local priority for 2019 and 2020. EC 1 EC 2 EC 3 EC 4 EC 5 EC 6 EC 7 EC 8 EC 9 EC 10 EC 11 EC 12 EC 13 EC 14 EC 15 EC 16 EC 17 EC 18 EC 19 wifor 2019 0.335 0.335 0.238 0.261 0.308 0.247 0.211 0.215 0.307 0.209 0.141 0.201 0.201 0.298 0.201 0.201 0.137 0.135 0.246 wifor 2020 0.136 0.343 0.246 0.300 0.019 0.108 0.219 0.242 0.111 0.116 0.150 0.201 0.348 0.122 0.219 0.122 0.243 0.240 0.346 At this point, we have defined the overall efficiency of the processes measured by the composite indicator defined with the formula (1). The CI values are shown in Table 5. Table 5. Composite indicator for 2019 and 2020. Process 1 Process 2 Process 3 Process 4 Process 5 Process 6 Process 7 Process 8 Process 9 2019 0.781 0.891 0.980 0.968 0.926 0.949 0 0.903 0.953 2020 0.595 0.961 0.989 0.985 0.979 0.902 0.679 0.569 0 As we can see, processes 3 and 4 are the more efficient in both 2019 and 2020. Some considerations can be made also on the variations from one year to the other, in order to evaluate the effectiveness of decisions made on the process’s execution. For example, for process 7 it is clear an improvement of the efficiency from 2019 to 2020, maybe thanks to some corrective actions performed on this process. On the other hand, process 9 has registered the worst variation, calling for an accurate analysis of the causes of the errors and for some significant adjustments. In order to better analyze the evolution over time of processes performance, we have calculated the Malmquist index (see, e.g., Malmquist 1953;Färe et al. 1994;Tone 2004), a common measure that has been widely adopted in several application domains (Wang et al. 2013 ,2014). Within our computational experience, we have considered the J. Risk Financial Manag. 2022,15, 293 15 of 15 Vesperi, Walter, Anna Maria Melina, Marzia Ventura, Raffaella Coppolino, and Rocco Reina. 2021. 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