Two-echelon collaborative multi-depot multi-period vehicle routing problem

Collaboration among logistics operators offers an effective way to improve customer service and freight transportation efficiency. One form of collaboration is the sharing of logistics resources (e.g., delivery vehicles). Existing studies on collaboration and resource sharing have not sufficiently accounted for the time frame within which collaboration happens, and they mostly assume that collaboration among logistics operators occurs in a single time period. This study addresses the issue of collaboration across multiple time periods, in which logistics resources can be shared between different service time periods, by formulating and solving a two-echelon collaborative multi-depot multi-period vehicle routing problem (2E-CMDPVRP). The 2E-CMDPVRP is formulated as a multi-objective integer programming model that minimizes logistics operational costs, service waiting times, and number of vehicles in multiple service periods. A hybrid heuristic algorithm with three-dimensional k-means clustering and improved reference point-based non-dominated sorting genetic algorithm-III (IR-NSGA-III) is proposed to solve the multi-objective optimization model. Comparative analysis results show that the proposed IR-NSGA-III outperforms existing algorithms in terms of the minimization of logistics operational costs, service waiting times, and number of vehicles. The minimum costs remaining saving method and strictly monotonic path selection principle are combined to determine the best profit allocation schemes and the optimal coalition sequences. An empirical case study of a multi-depot multi-period logistics network in Chongqing, China, is used to validate the proposed model and solution algorithm. Results suggest that the proposed collaborative mechanism with multi-depot and multi-period resource sharing can improve the degree of synchronization within a collaborative logistics network, and thus contribute to sustainable development of urban logistics distribution networks.