Energy Saving-Oriented Multi-Depot Vehicle Routing Problem with Time Windows in Disaster Relief

This paper studies the distribution of emergency relief for electric vehicles (EVs), which considers energy saving, multi-depot, and vehicle routing problems with time windows, and the named energy saving-oriented multi-depot vehicle routing problem with time windows (ESMDVRPTW). Our aim is to find routes for EVs such that all the shelter demands are fulfilled during their time windows and the total cost traveled by the fleet is minimized. To this end, we formulate the ESMDVRPTW as a mixed-integer linear programming model. Since the post-disaster transportation network contains a large number of vertices and arcs composed of vertices, we propose a two-stage approach to solve the ESMDVRPTW. The first stage is to obtain the minimal travel cost between any two vertices in real-time on a post-disaster transportation network using the proposed Floyd algorithm combined with the neighboring list (Floyd-NL algorithm). In the second stage, we develop the genetic algorithm (GA) incorporating large neighborhood search (GA-LNS), which determines the delivery scheme of shelters. Simulation results of the MDVRPTW benchmark illustrate that the performance of the GA-LNS is better than GA, simulated annealing (SA) and tabu search (TS). Finally, case studies are constructed on two real cases acquired from the OpenStreetMap (OSM) generated by the Quantum Geographic Information System (QGIS) in Ichihara city, Japan, and the test results of case studies show the effectiveness of the proposed two-stage approach.