Multi-mode hybrid electric vehicle routing problem

Hybrid electric vehicles (HEVs) are environmental-friendly vehicles that use a combination of the electric engine and internal combustion engine in their propulsion systems to reduce the fuel consumption and emission. In this paper, we consider a fleet of HEVs in logistics operations and introduce the Hybrid Electric Vehicle Routing Problem (HEVRP). Since we allow HEVs to operate in different drive modes, we refer to this problem as the Multi-Mode HEVRP (MM-HEVRP). We first model the problem as a mixed-integer linear program, where the objective function mini-mizes the total cost of the distances traveled at different modes. Since the problem is not trac-table, we develop a matheuristic approach to solve it. The proposed approach combines Variable Neighborhood Search with mathematical programming. We test the performance of the proposed approach by solving benchmark instances generated for the Hybrid Electric Vehicle-Traveling Salesman Problem (HEV-TSP) and comparing our results with those published in the literature. In addition, we generate new MM-HEVRP data by modifying HEV-TSP benchmark instances. We solve the small-size MM-HEVRP instances using CPLEX and compare our solutions with the optimal solutions. The numerical results show that the proposed matheuristic is able to achieve high-quality solutions with reasonable computation times. Furthermore, we address the large-size instances and present a sensitivity analysis to provide further insights.