Cooperation and profit allocation for two-echelon logistics pickup and delivery problems with state–space–time networks

Abstract

Cooperation is a powerful strategy to reduce the costs of pickup and delivery services in the conventional two-echelon pickup and delivery problems (2E-PDPs). This study develops a cooperative 2E-PDP with state–space–time network (C2E-PDPSST) and incorporates vehicle routing problem and profit allocation optimization. Transportation resource sharing (trucks/vehicles) is presented as a major cooperative strategy in C2E-PDPSST to reduce the number of vehicles and improve resource utilization. A bi-objective mixed integer model is proposed to minimize total operating costs and number of vehicles and is formulated based on state–space–time networks. A novel methodology, which combines the time-dependent forward dynamic programming algorithm and a hybrid heuristic algorithm comprising modified k-means clustering algorithm and improved multi-objective particle swarm optimization (IMOPSO) algorithm, is designed for solving C2E-PDPSST. The clustering process speeds up the solution by reducing the computational complexity. The IMOPSO algorithm combines inter- and intra-route operations to find the Pareto optimal solutions with predefined iteration and termination rules. The inter-route operations will improve the population diversity, while the intra-route operations will generate an optimal solution for each vehicle route. Thus, an effective combination of local and global solution search can be achieved. Profit allocation schemes are investigated using the criteria of minimum cost remaining savings. Our results on benchmark instances show that the proposed IMOPSO has better computational performance than the conventional MOPSO and multi-objective genetic algorithm. A case study based on the realistic logistics network in Chengdu City, China is conducted for validation. The proposed methodology considering state–space–time network performs better in terms of reducing traveling costs, and improving the flexibility and efficiency of the entire network.