Multi-depot green vehicle routing problem with shared transportation resource: Integration of time-dependent speed and piecewise penalty cost

Abstract The control of the environmental impacts is a considerable challenge to the daily operations of modern logistics companies, especially under the current trend of increasing carbon dioxide emission. This paper focusses on freight distribution, introduces a transportation resource sharing strategy to address the multi-depot green vehicle routing problem, and incorporates the time-dependency of speed as well as piecewise penalty costs for earliness and tardiness of deliveries. Transportation resource sharing is proposed to eliminate long and empty-vehicle trips, improve the network's fluidity and the efficiency of resource management. A bi-objective model is proposed to minimize total carbon emission and operating cost, while enforcing piecewise penalty costs on earliness and tardiness to reduce waiting time and improve customer satisfaction. Further, we combine the Clarke and Wright Savings Heuristic Algorithm (CWSHA), the Sweep Algorithm (SwA) and the Multi-Objective Particle Swarm Optimization algorithm (MOPSO) to design a hybrid heuristic algorithm for the vehicle routing optimization. CWSHA and SwA are consecutively used to generate the initial population, and MOPSO is employed for local and global solution search. Computational experiments reveal that sharing transportation resource reduces the total travelled distance, the number of vehicles, and facilitates a cost effective and environment-friendly distribution network. In addition, we also observe that the shortest path sometimes undermines minimum cost and carbon emission objectives. Moreover, sensitivity analyses reveal that vehicle routes are less influenced by piecewise penalty costs under unimodal traffic flows, while bimodal traffic flows would require more investment to reduce carbon emission.