Integrated optimization of logistics routing problem considering chance preference

Ren, Liang; Zhou, Zerong; Fu, Yaping; Liu, Ao; Ma, Yunfeng Article Integrated optimization of logistics routing problem considering chance preference Modern Supply Chain Research and Applications Provided in Cooperation with: Emerald Publishing Limited Suggested Citation: Ren, Liang; Zhou, Zerong; Fu, Yaping; Liu, Ao; Ma, Yunfeng (2024) : Integrated optimization of logistics routing problem considering chance preference, Modern Supply Chain Research and Applications, ISSN 2631-3871, Emerald, Bingley, Vol. 6, Iss. 4, pp. 376-392, https://doi.org/10.1108/MSCRA-05-2023-0016 This Version is available at: https://hdl.handle.net/10419/314932 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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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by/4.0/ Integrated optimization of logistics routing problem considering chance preference Liang Ren School of Management, Wuhan University of Science and Technology, Wuhan, China and Center for Service Science and Engineering, Wuhan University of Science and Technology, Wuhan, China Zerong Zhou School of Management, Wuhan University of Science and Technology, Wuhan, China Yaping Fu College Business, Qingdao University, Qingdao, China, and Ao Liu and Yunfeng Ma School of Management, Wuhan University of Science and Technology, Wuhan, China and Center for Service Science and Engineering, Wuhan University of Science and Technology, Wuhan, China Abstract Purpose –This study aims to examine the impact of the decision makers’ risk preference on logistics routing problem, contributing to logistics behavior analysis and route integration optimization under uncertain environment. Due to the unexpected events and complex environment in modern logistics operations, the logistics process is full of uncertainty. Based on the chance function of satisfying the transportation time and cost requirements, this paper focuses on the fourth party logistics routing integrated optimization problem considering the chance preference of decision makers from the perspective of satisfaction. Design/methodology/approach –This study used the quantitative method to investigate the relationship between route decision making and human behavior. The cumulative prospect theory is used to describe the loss, gain and utility function based on confidence levels. A mathematical model and an improved ant colony algorithm are employed to solve the problems. Numerical examples show the effectiveness of the proposed model and algorithm. Findings –The study’s findings reveal that the dual-population improvement strategy enhances the algorithm’s global search capability and the improved algorithm can solve the risk model quickly, verifying the effectiveness of the improvement method. Moreover, the decision-maker is more sensitive to losses, and the utility obtained when considering decision-makers’ risk attitudes is greater than that obtained when the decision-maker exhibits risk neutrality. Practical implications –In an uncertain environment, the logistics decision maker’s risk preference directly affects decision making. Different parameter combinations in the proposed model could be set for decisionMSCRA 6,4 376 © Liang Ren, Zerong Zhou, Yaping Fu, Ao Liu and Yunfeng Ma. Published in Modern Supply Chain Research and Applications. Published by Emerald Publishing Limited. This article is published under the Creative Commons Attribution (CC BY 4.0) licence. Anyone may reproduce, distribute, translate and create derivative works of this article (for both commercial and non-commercial purposes), subject to full attribution to the original publication and authors. The full terms of this licence may be seen at http://creativecommons.org/licences/by/4.0/legalcode This work is supported by the Natural Science Foundation of Hubei Province of China under Grant No. 2020CFB142; the Hubei Province Department of Education Humanities and Social Sciences Research Project under Grant No. 20Q21; Foundation of WUST Research on Development of Smart Logistics Digital Operation Platform under Grant No. 2022H20537. The current issue and full text archive of this journal is available on Emerald Insight at: https://www.emerald.com/insight/2631-3871.htm Received 1 May 2023 Revised 27 January 2024 16 April 2024 2 August 2024 Accepted 20 August 2024 Modern Supply Chain Research and Applications Vol. 6 No. 4, 2024 pp. 376-392 Emerald Publishing Limited 2631-3871 DOI 10.1108/MSCRA-05-2023-0016 makers with different risk attitudes to fit their needs more accurately. This could help managers design effective transportation plans and improve service levels. In addition, the improved algorithm can solve the proposed problem quickly, stably and effectively, so as to help the decision maker to make the logistics path decision quickly according to the required confidence level. Originality/value –Considering the uncertainty in logistics and the risk behavior of decision makers, this paper studies integrated routing problem from the perspective of opportunity preference. Based on the chance function of satisfying the transportation time and cost requirements, a fourth party logistics routing integrated optimization problem model considering the chance preference of decision makers is established. According to the characteristics of the problem, an improved dual-population ant colony algorithm is designed to solve the proposed model. Numerical examples show the effectiveness the proposed methods. Keywords Fourth party logistics, Routing optimization, Dependent-chance programming, Ant colony algorithm, Risk attitude Paper type Research paper 1. Introduction With the rapid development of modern economy and e-commerce, the competition among modern enterprises is becoming more and more fierce (Tian et al., 2022;Fu et al., 2021a,b). As an important means of promoting enterprise industrial upgrading and enhancing core competitiveness, logistics has attracted widespread attention from various industries (Stodola, 2020;Goli et al., 2022). At the same time, people’s demands for logistics service levels have continued to increase (Qian et al., 2021;Mehmann and Teuteberg, 2016), particularly in uncertain logistics services where stable and efficient delivery is one of the most effective ways for modern logistics companies to win customer recognition. In order to improve logistics efficiency and core competitiveness of enterprises, most enterprises outsource logistics business to professional third-party logistics (3PL) providers. However, with the rapid development of modern logistics, customers’ requirements for logistics service level are constantly increasing. Logistics decision is not only about accomplishing transportation tasks, but also resource sharing and ability integration among different subjects (Wang et al., 2020,2024). Traditional 3PL providers lack supply chain management capabilities, and the cooperation between 3PL providers is not deep enough, and complementary resources are not fully utilized, making it difficult to meet the current market demand for fierce competition (Zhang et al., 2021). Therefore, the industry and academia are both focusing on fourth-party logistics (4PL) from a resource integration perspective (Gattorna, 1998;Yao, 2010). In recent years, 4PL companies and logistics enterprises formed and providing services based on the 4PL concept have gradually demonstrated their strong competitiveness and influence (Huang et al., 2009). The essential nature and core advantage of 4PL operation lie in its ability to integrate supply chain resources (Tao et al., 2017). By cooperating with participants at various stages within the supply chain, 4PL can facilitate mutual promotion, alleviate the phenomenon of 3PL enterprises acting alone, vicious competition in developed areas and inadequate supply in underdeveloped areas, and effectively integrate and fully utilize social resources (Yin et al., 2022). Many scholars at home and abroad have conducted research on issues related to 4PL, such as supplier evaluation problems (Krakovics et al., 2008), 3PL supplier selection (Aguezzoul, 2014), contract design (Wang et al., 2021;Huang et al., 2019), scheduling (Liu et al., 2014), network design (Wang et al., 2021), routing problem (Zhang et al., 2005) and so on. Route planning is one of the core factors affecting the overall efficiency of logistics (Goli et al., 2022;Wang et al., 2023). The fourth party logistics routing optimization problem (4PLROP) is a critical issue in modern logistics optimization (Huang et al., 2016). 4PL involves selecting appropriate transportation routes for shipping tasks while also selecting the 3PL suppliers who provide transportation services along that path, presenting a challenge to traditional routing problems. Some scholars have proposed simplifying 4PLROP by using a Modern Supply Chain Research and Applications 377 description method of a directed multigraph. Chen et al. (2003) described each edge in a directed multigraph as a 3PL supplier that provides transportation services along that path, providing a clear description of 4PLROP and quickly solving small-scale problems. Cui et al. (2013) integrated path selection and 3PL supplier selection into an undirected multigraph, also describing each edge in the graph as a 3PL supplier, and studied the more complex 4PLROP while considering issues such as transfer truck time and multitasking. Most existing relevant research has focused on deterministic problems. However, due to factors such as weather, traffic, human error and various unexpected situations, logistics transportation processes have strong uncertainty (Huang et al., 2015), which caused substantial losses in profits (Zhou et al., 2023;Goli et al., 2023a,b). Especially in long-distance delivery such as cross-border transportation, there are significant disturbances in logistics transportation time and cost due to geography, relevant systems and language reasons. Huang et al. (2013) assumed that the 4PL system had no historical data, so the distribution of 3PL supplier transportation time could be described as a fuzzy variable by relevant experts based on historical experience, and studied the 4PLROP with fuzzy processing time with the objective of minimizing total cost. However, in another scenario in logistics operations, logistics companies have some historical data, which can be used to estimate the probability or probability distribution of uncertain events using random variables. Moreover, with the rapid development of e-commerce and fierce competition in the logistics industry in recent years, traditional price competition between logistics companies has gradually shifted to competition based on customer service levels (Fu et al., 2020,2021a,b). In an uncertain environment, decision-makers often hope to maximize the probability function of event realization (Liu, 1997), rather than absolute returns, and hope to achieve higher customer satisfaction while ensuring a certain return. In order to accurately describe and measure the characteristics of people’s cognition, judgment and choice in uncertain situations, Simon (1955) proposed the theory of bounded rationality. On this basis, Tversky and Kahneman (1992) proposed the Prospect theory. Prospect theory applies psychological research to economics and provides an effective tool for human judgment and decision making under uncertain environment. This study describes the transportation time and cost of 3PL suppliers as random variables and investigates the 4PLROP in an uncertain environment. As the scheme designer, 4PL hopes to minimize the probability of delay from the customer’s perspective, while also minimizing the probability of exceeding cost expectations from the perspective of the participating 3PL suppliers. Therefore, depending on the risk attitude of the decision-maker, this study establishes a mathematical model for the Dependent-chance based 4PL Routing Optimization Problem (DP-4PLROP) by maximizing the total utility of the transportation time and cost opportunity functions, taking into account attitude towards opportunities. The proposed DP4PLROP is an NP-hard problem, which is difficult to be solved by traditional algorithms. Intelligent optimization algorithm is one of the effective ways to solve large-scale complex optimization problems (Goli et al., 2023b;Wang et al., 2022). Based on the characteristics of the problem, ant colony algorithms and dual-population improved ant colony algorithms are designed to solve the model. The numerical examples demonstrate the rationality of the established model and the effectiveness of the proposed algorithm. 2. Problem description Assuming a certain company (4PL) has undertaken a supply chain logistics path integration business, it is required to design a set of transportation plans for the client which will transport transportation tasks from the starting point of the supply chain to the destination node. Since 4PL is a logistics solution integrator, it is assumed that it has certain path information and some cooperating 3PL suppliers before the task starts. The transportation MSCRA 6,4 378 network information and alternative 3PL suppliers’ information in the supply chain are known, and there may be multiple 3PL suppliers that can provide transportation services along each path. In order to describe the problem more clearly, supplier information and path information are integrated. The proposed DP-4PLROP can be described by a multi-graph with multiple attributes. An undirected multigraph GðV;EÞshown in Figure 1 is used to describe the proposed DP4PLROP. VðjVj ¼ nÞis the set of nodes, representing cities, warehouses, processing plants and other facilities in the supply chain; E is the set of edges, each edge represents a candidate 3PL supplier who can undertake transportation tasks on that path, and there may be multiple edges between adjacent nodes. Both nodes and edges have cost and time attributes. Due to various uncertain factors in logistics transportation, the transportation time and cost of the 3PL supplier have a certain degree of disturbance, which is described as a random variable. The parameters and decision variables of the DP-4PLROP based on the description of the undirected multigraph are presented in Table 1. s e 4 3 2 1 5 2 2 2 1 2 2 2 2 2 2 2 2 1 3 1 3 1 4 1 1 3 4 1 3 11 3 1 1 3 2 1 3 Source(s): Authors’ own work Parameters eijk Represents the kth 3PL supplier (kth edge) between nodes viand vj, i;j∈ð1;2;���;nÞ rij Represents the number of 3PL suppliers (edges) between nodes viand vj Tijk þtijk Represents the time between nodes viand vjfor 3PL supplier eijk to complete the transportation task of this section. Where, Tijk is constant and represents basic time; tijk is a random variable, representing the disturbance of time Cijk þcijk Represents the cost required by 3PL supplier eijk to complete this section of transportation task. Where Cijk is constant, representing basic cost; cijk is a random variable representing the perturbation of cost T0 i;C0 iRepresents the time and cost required by the transportation task when it passes through node vi, respectively T0;C0Respectively represents the decision-maker’s requirements on the total time and total cost of the transportation task, that is, the total transportation time should not exceed T0and the total transportation cost should not exceed C0 α ;βThe confidence level indicating the total time and total cost that meet the requirements separately, that is, in an uncertain environment, the probability that the total transportation time does not exceed T0and the probability that the total transportation cost is not greater than C0 R It represents a path from the starting node vsto the destination node veof a task Decision variable eijkðRÞ1 if eijk ∈R, 0 otherwise yiðRÞ1 if vi∈R, 0 otherwise Source(s): Authors’ own work Figure 1. Multi-graph of DP4PLROP Table 1. Mathematical notation Modern Supply Chain Research and Applications 379 Here, tijk and cijk respectively represent the disturbance of transportation time and cost of 3PL supplier eijk. For the purpose of exposition and necessary mathematical simplification, it is assumed that they follow normal distributions Nð0; σ 2 ijkÞand Nð0; σ 2 ijkÞ, and are independent of each other [1]. It can be seen that R is the solution to the proposed problem. In the multi-graph, each R uniquely determines the path taken by the transportation task and the 3PL supplier who performs the transportation task on that path. The time and cost of Rare represented by TðRÞ and CðRÞrespectively, then: TðRÞ ¼ X n i¼1X n j¼1X rij k¼1ðTijk þtijkÞxijkðRÞþX n i¼1 T0 iyiðRÞ;(1) CðRÞ ¼ X n i¼1X n j¼1X rij k¼1ðCijk þcijkÞxijkðRÞþX n i¼1 C0 iyiðRÞ:(2) Therefore, TðRÞand CðRÞalso follow normal distributions, that is TðRÞ∼N X n i¼1X n j¼1X rij k¼1 TijkxijkðRÞþX n i¼1 T0 iyiðRÞ;X n i¼1X n j¼1X rij k¼1 σ 2 ijkxijkðRÞ!; CðRÞ∼N X n i¼1X n j¼1X rij k¼1 CijkxijkðRÞþX n i¼1 C0 iyiðRÞ;X n i¼1X n j¼1X rij k¼1 σ 2 ijkxijkðRÞ!: The problem to be solved in this paper is to provide customers with a transportation plan that transports transportation tasks from the starting node to the destination node under certain time and cost requirements. Due to the disturbance of transportation time and cost of 3PL suppliers, the plan meets the total time and total cost requirements with a certain confidence level, and maximizes the total utility of the confidence level while considering the decision maker’s preference. 3. Problem formulation For a given path R, its total time TðRÞand total cost CðRÞsatisfy the confidence levels α and β (opportunity function) required by the customer, as shown in Eq. (3) and Eq. (4). α ¼Pr(X n i¼1X n j¼1X rij k¼1ðTijk þtijkÞxijkðRÞþX n i¼1 T0 iyiðRÞ≤T0)(3) β¼Pr(X n i¼1X n j¼1X rij k¼1ðCijk þcijkÞxijkðRÞþX n i¼1 C0 iyiðRÞ≤C0)(4) People often pay more attention to differences rather than absolute return values when making decisions (Tversky and Kahneman, 1992). Therefore, we first assume that the decision maker has expectations for the confidence levels of total time and total cost, which are the reference points α 0and β0. For each alternative plan R, it represents a loss when the confidence level is below the reference point, and a gain when the confidence level is above the reference point. Thus, drawing on the value function description in cumulative prospect theory (CPT) (Tversky and Kahneman, 1992), the utility functions of total time and total cost can be defined as follows: MSCRA 6,4 380 vð α Þ ¼ �ð α � α 0Þγ1;if α ≥ α 0 �λ1ð α 0� α Þγ1;else (5) vðβÞ ¼ �ðβ�β0Þγ2;if β≥β0 �λ2ðβ0�βÞγ2;else (6) Here, the parameters γ1and γ2represent the sensitivity of the decision maker to the confidence levels of time and cost, with larger values indicating greater sensitivity. Moreover, 0 <γ1<1;0<γ2<1, which reflects the general characteristic of decreasing sensitivity of the decision maker. The parameters λ1and λ2are the relative sensitivity coefficients for gain and loss, with higher values indicating a stronger aversion to losses. In addition, the relative values of γ1,λ1and γ2,λ2can reflect the relative sensitivity of the decision maker to the confidence levels of time and cost. In an uncertain environment, the mathematical model for DP-4PLROP can be established as follows: maxfV¼vð α ÞþvðβÞg (7) s.t. xijkðRÞ ¼ �1;if eijk ∈R 0;else (8) yiðRÞ ¼ �1;if vi∈R 0;else (9) R¼ ðvs;���;vi;k;vj;���;veÞ∈G (10) Among them, formula (7) is the objective function, which represents maximizing the total utility of the confidence levels for time and cost. The confidence levels α and βare expressed in formulas (3) and (4), respectively, and the utility functions vð α Þand vðβÞare expressed in formulas (5) and (6), respectively. Formulas (8) and (9) are the 0–1 decision variables of the model, which determine the selected 3PL provider for executing the task and the nodes passed through. Formula (10) indicates that the selected path is a route from the starting node to the destination node. 4. Algorithm design 4.1 Design idea It can be seen that DP-4PLROP is an extension of the Constrained Shortest Path Problem (CSPP). CSPP is an NP-hard problem (Liu et al., 2012), and therefore DP-4PLROP is also NPhard, making it difficult to solve using traditional exact algorithms (Fu et al., 2022;Tian et al., 2023). The Ant Colony Algorithm (ACA) is an intelligent algorithm that mimics the behavior of ant colonies. It has high robustness, distributed computing and is easily combinable with other optimization methods, especially when solving shortest path problems such as VRP and TSP, showing unique advantages (Dorigo et al., 1996). Considering the problem of premature convergence and stagnation in ACA during evolution, an Improved Ant Colony Algorithm (IACA) is designed by incorporating the idea of dual-population independent searching with periodic information exchange based on the characteristics of undirected multigraphs. Modern Supply Chain Research and Applications 381 4.2 ACA (1) Coding mechanism Ris the solution to the problem, representing a path from the starting node vsto the destination node vein a multi-graph. It includes a set of edges and a set of nodes. From the multigraph description, it can be seen that each edge eijk uniquely determines a pair of adjacent nodes vi and vjin R, that is, the set of edges in Rcan uniquely determine the set of nodes. Therefore, only the set of edges is encoded. Considering that the number of edges in each solution may vary, a variable-length encoding mechanism is designed. NP represents the population size, and the coding of the mth ðm¼1;2;���;NPÞant can be represented as follows: Rm¼ ðesik;���;ejelÞ∈G:(11) Here, esik represents the starting node vsof Rm, ejel represents the final destination node ve.In order to ensure the connectivity of Rm, adjacent elements (edges) must pass through the same intermediate node, that is, the arrival node of the previous element and the entry node of the next element are the same. (2) Transfer probability During the transfer process of ant m, its direction is determined based on the information on all feasible edges and the path heuristic information. Let NGrepresent the maximum number of iterations, and allowedmrepresent the set of all feasible edges for ant m at the current moment. Then, the calculation method for the transfer probability pm ijkðNgÞof a certain edge eijk in the current feasible set at the NgðNg ¼1;2;���;NGÞiteration is as follows: pm ijkðNgÞ ¼ ½ τ ijkðNgÞ� ω � η ijk�φ Xarc⊂allowedm½ τ arcðNgÞ� ω ½ η arc�φ 0;else ;arc ∈allowedm: 8 > > > < > > > : (12) Here, τ ijkðNgÞrepresents the concentration of information pheromones on edge eijk in the Ng-th iteration, η ijk represents the path heuristic information, where η ijk ¼1=ðTijk þCijkÞ. ω and φ respectively represent the pheromone heuristic factor and path heuristic factor, reflecting the relative importance of information pheromone concentration and path heuristic information. (3) Pheromone updating strategy At the beginning of algorithm execution, the same initial information pheromone concentration P0is assigned to each edge in the multi-graph. After every generation of ants completes the search, the pheromone concentration is updated using the following formula: τ ijkðNg þ1Þ ¼ ρτ ijkðNgÞþ∆ τ ijk (13) ∆ τ ijk ¼8 > < > : α þβþθv Q;eijk ∈R 0;else (14) Here, τ ijkðNg þ1Þrepresents the concentration of information pheromones on edge eijk in the iteration of ðNg þ1Þ,∆ τ ijk represents the increment of pheromone concentration, R MSCRA 6,4 382 represents the current optimal solution, v represents the current optimal value and θis a constant when v≥0, but θ¼0 when v <0. (4) Maximum and minimum ant As the algorithm iterates, it is possible for the concentration of information pheromones on certain paths in the multi-graph to continuously increase, while pheromones on other paths continuously evaporate. To avoid highly concentrated pheromone levels that cause all ants in the population to search the same path, leading to premature convergence to a local optimum, the concentration of pheromones on each edge is limited to a certain range. When τ ijkðNgÞ< τ min, τ ijkðNgÞ ¼ τ min; when τ ijkðNgÞ> τ max, τ ijkðNgÞ ¼ τ max. (5) Repair strategy of illegal paths During the ant search process, there may be a situation where the current feasible set allowedmis empty, which means that there is no valid path to reach the destination node. In this case, it is necessary to repair the invalid path. The traditional method is for the ant to backtrack to the previous node and add the current path to the taboo list. However, this method consumes a lot of computational time due to the backtracking process. Therefore, according to the characteristics of the problem, the following method is designed for repairing invalid paths: for the current invalid path Rm, starting from its initial node, check whether the current node is directly connected to the destination node in the multi-graph. If it is, randomly select an edge between the node and the destination node and add it to the encoding; otherwise, the ant restarts the search. 4.3 IACA ACA often shows unique advantages in solving routing problems (Dorigo et al., 1996). However, premature convergence and stagnation often cause the algorithm to fail to obtain optimal solutions. To address this problem and solve the proposed model quickly and efficiently, a dual-population independent evolution approach is designed. In IACA, two populations evolve independently and regularly interact with each other, to prevent local convergent behavior of single-population search and improve the global search capability. (1) The update method of pheromone for population A In the multi-graph, each edge eijk has two types of pheromones, τ A ijkðNgÞand τ B ijkðNgÞ, which represent the pheromone concentration of populations A and B, respectively, in the Ng-th generation. Population A uses the elite strategy to update pheromones, as shown in equations (13) and (14). (2) The update method of pheromone for population B In population B, pheromone is updated based on the fixed amount of pheromone left by each ant on the path it has passed through, and the update formula is as follows: τ B ijkðNg þ1Þ ¼ ρτ B ijkðNgÞþ μ ∆ τ ;(15) In which μ represents the number of ants passing through the edge eijk in the Ng-th generation, and ∆ τ is the pheromone left by the ants as they pass by. (3) Pheromone interaction When the iteration number Ng is a multiple of M, the pheromone interaction between population A and population B is performed. 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Corresponding author Zerong Zhou can be contacted at: [email protected] For instructions on how to order reprints of this article, please visit our website: www.emeraldgrouppublishing.com/licensing/reprints.htm Or contact us for further details: [email protected] MSCRA 6,4 392