Two-echelon multi-period location routing problem with shared transportation resource

Abstract Solving a two-echelon multi-period location routing problem (2E-MPLRP) involves facility location selection and two-echelon vehicle routing optimization. Based on the periodic time characteristics of logistics facilities and customers, the optimal solutions provide periodic location decisions and vehicle routing schemes simultaneously in each service period of the planning horizon. Transportation resource configuration is tweaked by enabling resource sharing across multiple service periods to maximize resource utilization in the context of growing emphasis on sustainable development. A bi-objective mathematical model is developed to formulate the 2E-MPLRP to obtain the minimum total operating cost and number of vehicles. A two-stage hybrid algorithm including three-dimensional (3D) k-means clustering and multi-objective improved particle swarm optimization (MOIPSO) algorithm is proposed to solve the 2E-MPLRP. The 3D k-means clustering algorithm is adapted to assign customers to distribution centers (DCs) to receive service in multiple service periods, and the MOIPSO algorithm is then designed to optimize the vehicle routes and find the Pareto optimal solutions. With an external repository strategy and a rapidly decreasing mutation strategy incorporated in the iterative process, the proposed hybrid algorithm performs well in expanding the particles’ searching region and achieving robust optimal results. An algorithm comparison demonstrates the superiority of the proposed hybrid algorithm over other existing algorithms. A real-world case study of 2E-MPLRP in Chongqing, China is conducted, and results show that the proposed model and algorithm are of practical significance in minimizing operating cost, improving transportation efficiency, and contributing to sustainable two-echelon logistics network operations.