Two-echelon collaborative multi-depot multi-period vehicle routing problem
Introduction
The multi-depot vehicle routing problem (MDVRP) focuses on optimizing vehicle routes to reduce logistics operational costs in multi-depot logistics networks (Wang et al., 2017, Li et al., 2018). In a traditional multi-depot distribution network, the delivery service of a product is assumed to repeat daily with a stable service level over a planning horizon (Dayarian et al., 2015, Dayarian et al., 2016). However, customer demand and service capacity change periodically in practice. For example, customer demands for different fresh products change with seasons, and the delivery time windows that logistics service providers can offer are not constant. According to the China Statistical Yearbook data in 2018 (CNBS, 2018), the per capita consumption of commodities with periodic demands increased by 20.6% since 2013; these commodities included the fruit products with seasonal productivity and the products with periodic price fluctuations. The multi-depot multi-period vehicle routing problem (MDPVRP) aims to satisfy customer demands with periodic changes and improve customer service levels in a multi-depot multi-period logistics network (Cantu-Funes, Salazar-Aguilar, & Boyer, 2018). As an extension of the traditional MDPVRP, the two-echelon multi-depot multi-period vehicle routing problem (2E-MDPVRP) accounts for collaboration and synchronization in logistics operations.
The rapid development of e-commerce and the resulting increase in logistics demands have strained transportation and other logistics resources. The Chinese National Bureau of Statistics (CNBS, 2019) reported that the average daily gasoline and diesel consumption in the transportation and warehousing system has increased by 77.4% in the past 10 years. The appropriate use of limited resources to satisfy as much customer demand as possible is the key to optimize the multi-depot multi-period network system. One way to optimize resource utilization and transportation efficiency is to develop effective synchronization and resource sharing strategies (Liu & Ceder, 2017). Synchronization involves coordinating vehicle schedules in large-scale logistics networks to reduce the service waiting time (Fonseca, van der Hurk, Roberti, & Larsen, 2018). Resource sharing is aimed at maximizing resource utilization (Yea, Chung, Cheong, & Kim, 2018). It can be achieved and incentivized by the establishment of a collaborative mechanism among multiple facilities in a logistics network, where resource sharing can be achieved among facilities in a single time period (Quintero-Araujo et al., 2017, Wang et al., 2018a, Adhikari and Bisi, 2020). Collaboration across multiple time periods, which can promote the resource sharing in multiple time periods and improve the resource utilization in the sustainable logistics network, is rarely discussed in existing research. Therefore, an effective collaborative mechanism must be incorporated in the two-echelon collaborative multi-depot multi-period vehicle routing problem (2E-CMDPVRP) to achieve maximum resource utilization and improve transportation efficiency.
In the present study, we focus on collaborative mechanism, synchronization, and resource sharing to optimize a two-echelon collaborative multi-depot multi-period logistics network (2E-CMDPLN). The collaborative mechanism is established among multiple facilities and periods to improve transportation efficiency and reduce logistics operational cost. Synchronization is leveraged to optimize vehicle scheduling and resource coordination. Resource sharing, such as customer information sharing and transportation sharing, is proposed to achieve reasonable resource configuration and maximum resource utilization. To address the 2E-CMDPVRP with synchronization and resource sharing, this study establishes a multi-objective integer programming model for reducing logistics operational costs, service waiting times, and number of vehicles in 2E-CMDPLN. Three-dimensional (3D) k-means clustering is employed to reassign customers to their adjacent distribution centers (DCs) on the basis of geographic coordinates and time windows. An improved reference point-based non-dominated sorting genetic algorithm III (IR-NSGA-III) is proposed to find the optimal Pareto solutions. A profit allocation method and a strictly monotonic path (SMP) strategy are devised to select the optimal coalition sequences and maintain coalition stability.
This work has the following novelty and contributions. (1) Collaborative mechanisms are proposed to coordinate resource configuration among multiple depots in a multi-period logistics network. (2) Synchronization and resource sharing are introduced in a two-echelon network to optimize vehicle schedules and thereby improve transportation efficiency and to encourage collaboration among multiple facilities across different time periods. (3) A multi-objective integer programming model is established to optimize vehicle routing in a 2E-CMDPLN under periodically varying customer demands. (4) A hybrid heuristic algorithm with 3D k-means clustering and the IR-NSGA-III is proposed and tested in a case study in Chongqing, China, and the proposed algorithm is found to be effective in finding the Pareto optimal solutions and determining the best vehicle routes over a multi-period horizon.
The remainder of this paper is presented as follows. Relevant studies are reviewed in Section 2, and the problem statement of the 2E-CMDPVRP is provided in Section 3. A multi-objective integer programming model and the related definitions are developed in Section 4. A solution methodology and a profit allocation strategy are proposed in Section 5. An empirical study conducted in Chongqing, China is discussed in Section 6 to demonstrate the applicability and validity of the solution methodology. The conclusions are summarized, and future research is discussed in Section 7.
Section snippets
Literature review
With the expansion of logistics networks and the increase of customer demands, designing optimized mechanisms has become the key to improving the efficiency of transportation systems. In existing studies, the multi-depot vehicle routing problem (MDVRP) and multi-period vehicle routing problem (MPVRP) were investigated to design the optimal routes for the optimization of multi-depot and multi-period logistics networks (Pérez-Bernabeu et al., 2014, Dayarian et al., 2015). As an extension of the
Problem statement
Relative to the traditional MDVRP and MPVRP, the 2E-CMDPVRP is defined to optimize multi-period customer service in a two-echelon multi-depot distribution network through collaboration and resource sharing. The two-echelon multi-depot multi-period logistics network is composed of logistics facilities, including a logistics center (LC) and multiple DCs, in the first echelon and a large number of customers to be served in the second echelon. Each logistics facility has different service time
Model formulation for 2E-CMDPVRP
The 2E-CMDPVRP focuses on optimizing multi-period customer service with minimum logistics operational cost and maximum resource utilization. Through collaboration among facilities and resource sharing, effective centralized transportation and vehicle scheduling are utilized to improve logistics network operational efficiency. Resource utilization can be improved by minimizing the service waiting time and number of vehicles on the basis of transportation resource sharing and synchronization
Hybrid heuristic algorithm
Many integrated hybrid heuristic algorithms are used to obtain the optimal solutions in solving the MDVRP, MDPVRP, and CMDVRP (Adelzadeh et al., 2014, Cantu-Funes, Salazar-Aguilar, & Boyer, 2018, Wang et al., 2020a). Therefore, a hybrid heuristic algorithm, which includes 3D k-means clustering and the IR-NSGA-III algorithm, is proposed to address the 2E-CMDPVRP. The 3D k-means clustering algorithm is used to reduce the computational complexity in large-scale logistics networks (
Algorithm comparison and analysis
To test the performance of the proposed IR-NSGA-II, we compare it with well-known heuristic algorithms for addressing the CMDPVRP, namely, multi-objective particle swarm optimization (MOPSO) (Zhang & Chen, 2016), multi-objective evolutionary algorithm (MOEA) (Yang, Jiang, & Yong, 2016), and NSGA-II (Nedjati, Izbirak, & Arkat, 2017). These existing algorithms have been widely used by researchers to deal with traditional and extended MOPs with high quality solutions (Lagos et al., 2016, Ding et
Conclusions
This study incorporates resource sharing and synchronization in 2E-CMDPLN optimization. The collaborative strategies among multiple logistics facilities and among multiple service periods are modeled to optimize operational efficiency and resource configuration. A multi-phase solution framework is constructed for the 2E-CMDPVRP. First, a multi-objective integer programming model is established to minimize the total logistics operational cost, service waiting time, and number of vehicles.
CRediT authorship contribution statement
Yong Wang: Conceptualization, Methodology, Software, Validation, Formal analysis, Investigation, Data curation, Writing - original draft, Writing - review & editing, Supervision, Project administration, Funding acquisition. Qin Li: Software, Validation, Formal analysis, Investigation, Data curation, Writing - original draft, Writing - review & editing. Xiangyang Guan: Conceptualization, Methodology, Formal analysis, Investigation, Data curation, Writing - original draft, Writing - review &
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
This research is supported by National Natural Science Foundation of China (Project No. 71871035), Humanity and Social Science Youth Foundation of Ministry of Education of China (No. 18YJC630189), Key Science and Technology Research Project of Chongqing Municipal Education Commission (KJZD-K202000702), Social Science Planning Foundation of Chongqing of China (2019YBGL054), and Key Project of Human Social Science of Chongqing Municipal Education Commission (20SKGH079), This research is supported
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