Two-echelon multi-depot multi-period location-routing problem with pickup and delivery

Efficient logistics network designs can contribute to operational cost savings and efficiency improvements. In this study, a two-echelon multi-depot multi-period location-routing problem with pickup and delivery (2EMDMPLRPPD) is proposed, seeking to construct a logistics network with high efficiency by optimizing periodic location decisions and routing schemes. On the basis of the changing time windows of customers and facilities, the proposed 2E-MDMPLRPPD explores their potential periodicity and divides the whole planning horizon into multiple periods for conducting location decisions and arranging customer services. Vehicle-sharing strategies, which encourage vehicles to be shared by facilities across multiple periods, have also been integrated into the 2EMDMPLRPPD optimization to improve resource utilization and sustainability. The 2E-MDMPLRPPD is formulated as a bi-objective mathematical model, with the minimization of the total operational cost and number of vehicles as the two objective functions. To solve the optimization model, this study develops a hybrid multiobjective particle swarm optimization (HMOPSO) algorithm and introduces a three-dimensional (3D) k-means clustering to assist the proposed hybrid algorithm. The 3D k-means is the key to providing initial feasible candidate location strategies and simplifying the logistics network, reducing the complexity and difficulty for the following further optimization by HMOPSO. The proposed HMOPSO, integrating the Clarke-Wright saving algorithm and variable neighborhood search (VNS) into the standard MOPSO, shows good performance in solving the proposed 2E-MDMPLRPPD optimization, which is demonstrated through an algorithm comparison with MOPSO, multi-objective VNS and non-dominated sorting genetic algorithm-II. Finally, the proposed model and algorithm are applied to a real-world case study of 2E-MDMPLRPPD in Chengdu, China. A two-period locationrouting strategy can achieve the best optimization results, and based on the period division and periodic location strategy, the operating cost and required vehicles can save $15,394 and 25, respectively. A series of comparative analyses in different period divisions and location selection scenarios are implemented, and the practical significance in cost-saving and efficiency improvements is verified. Thus, this study can provide insights for logistics enterprises and facilitate sustainable and efficient urban logistics operations.