Collaborative multicenter vehicle routing problem with time windows and mixed deliveries and pickups

This study focuses on the collaborative multicenter vehicle routing problem with time windows and mixed deliveries and pickups (CMVRPTWMDP), which is a variant of the vehicle routing problem (VRP) with mixed deliveries and pickups, and VRP with simultaneous deliveries and pickups and time windows. Collaboration and transportation resource sharing are adopted to optimize vehicle routes in the CMVRPTWMDP, to integrate the delivery and pickup services with time windows, and to construct open–closed mixed vehicle routes. First, the CMVRPTWMDP is formulated as a mixed-integer programming model to minimize logistics operating costs. The effect of transportation resource sharing on reducing the number of needed vehicles and the maintenance cost is considered in the model formulation. Second, a two-stage hybrid algorithm combining customer clustering and vehicle routing optimization is designed to solve the CMVRPTWMDP. An improved 3D k-means clustering algorithm based on space–time distances and the customer demand is proposed to reassign customers to logistics facilities (e.g., delivery or pickup centers). Furthermore, a hybrid heuristic algorithm that combines the genetic algorithm (GA) and particle swarm optimization (PSO) algorithm, called GA–PSO, is designed to optimize the vehicle routes. A coordination operator between GA and PSO is designed to allow particles and chromosomes to interact, increasing the diversity of particle swarms and the possibility of finding a feasible solution. Third, the performance and effectiveness of the proposed approach are tested by comparing them with the CPLEX solver using 30 small-scale instances and other existing algorithms using 25 benchmark instances. Fourth, the minimum costs-remaining savings (MCRS) model is adopted to design a fair and reasonable profit allocation scheme for participants in the collaborative alliance and maintain alliance stability. Finally, the optimization results of a real-world case study from Chongqing, China, show that transportation resource misuse and logistics operating costs are significantly reduced, demonstrating the proposed approach’s effectiveness and applicability. This study provides insights for logistics enterprises and transportation departments on effectively allocating and utilizing the transportation resources and optimizing the local logistics network.