A heterogeneous fleet electric vehicle routing model with soft time windows

The emergence of electric vehicles in distribution and logistics activities has brought significant benefits due to their unique characteristics, such as energy-efficient and lower carbon emissions. In the perspective of vehicle routing problem, electric vehicles pose challenging constraints regarding the limited battery capacity, and thus their traveling ranges, and the availability of charging stations. In this paper, we propose a model of the fleet electric vehicle routing problem (EVRP) with soft time windows, where a mixed integer linear programming framework is implemented in model formulation. The objective of mathematical programming is to minimize the total operational cost, which consists of a fixed cost, a traveling cost, a battery charging cost, and probably a penalty cost due to time window violation. We implement our model in two simple cases, namely homogeneous and heterogeneous fleets EVRPs, characterized by loading and battery capacities. Each case consists of one depot, five customers, two electric vehicles, and two charging stations. Optimal routes are obtained using the well-known branch-and-bound method under Lingo 17.0. It is found that the existence of charging stations may affect the routes selection and the implementation of soft time windows rather than hard time windows has been proven to increase the feasibility of routing problem.