A Fuzzy Bi-objective Mathematical Model for Multi-depot Electric Vehicle Location Routing Problem with Time Windows and Simultaneous Delivery and Pick-up

Abstract

In green logistics, environmentally-friendly vehicles are strongly recommended as a transportation option. One of the green logistics vehicles is the electric vehicle which is a good selection to reduce greenhouse gas emissions. The present paper focused on the location-routing problem in electric vehicles by considering multi-depots and hard and soft time windows in uncertain conditions. We proposed a fuzzy bi-objective mathematical model for electric vehicles with a limitation in charge stations, the dependence of energy consumption to vehicle load, and a simultaneous delivery and pick-up. We used the multi-objectives particle swarm meta-heuristic algorithms based on the Pareto archive and the NSGA-II algorithm to solve this model. To evaluate the validity of the proposed model and algorithms, sample problems of EVRPTW were selected and solved using Gomez software and proposed meta-heuristic algorithms. The validation results for the model and algorithm confirmed that the model is valid, and the salving algorithms can solve the model efficiently and converge to an optimal answer. The comparing results of solving algorithms performance showed that, compared to the NSGA-II algorithm, the MOPSO algorithm has a higher ability in all states to generate higher quality responses and more diversity.