Electric Vehicle Scheduling and Optimal Charging Problem: Complexity, Exact and Heuristic Approaches

This paper deals with the Electric Vehicle Scheduling and Optimal Charging Problem. More precisely, given a fleet of Electric Vehicles EVs and Combustion Engine Vehicles CVs, a set of tours to be processed by vehicles and a charging infrastructure, the problem aims to optimize the assignment of vehicles to tours and minimize the charging cost of EVs, while considering several operational constraints mainly related to chargers, electricity grid, and EVs driving range. We prove that the Electric Vehicle Scheduling and Charging Problem (EVSCP) is NP-hard in the ordinary sense. We provide a mixed-integer linear programming formulation to model the EVSCP and use CPLEX to solve small and medium instances. To solve large instances, we propose two heuristics: a Sequential Heuristic SH and a Global Heuristic GH. The SH considers the EVs sequentially. To each EV, it assigns a set of tours and guarantees the feasibility of a charging schedule using the Maximum Weight Clique Problem. Then, it generates an optimal charging schedule for this EV using a Minimum Cost Flow formulation. However, the GH computes, in the first step, a feasible assignment of tours to all EVs. In the second step, it applies a global Min-Cost-Flow-based charging algorithm to minimize the charging cost of the EVs fleet. To evaluate the efficiency of our solving approaches, computational results on a large set of real and randomly generated test instances are reported and compared. Tested instances include large random instances with up to 200 EVs and 320 tours.