Multi-Objective Vehicle Routing Problem for a Mixed Fleet of Electric and Conventional Vehicles with Time Windows and Recharging Stations

The vehicle routing problem as a challenging decision problem has been studied extensively. More specifically, solving it for a mixed fleet requires realistic calculation of the performance of electric and combustion vehicles. This study addresses a new variant of the vehicle routing problem for a mixed fleet of electric and combustion vehicles under the presence of time windows and charging stations. A bi-objective mixed-integer programming model is developed which aims at minimizing cost and pollution level concurrently. To accurately quantify travel quantities, such as fuel consumption, emission, and battery charge level, a set of realistic mathematical formulas are used. The model is first converted to a single-objective counterpart using the epsilon-constraint method and a simulated annealing algorithm is tailored to obtain Pareto optimal solutions. A discussion is also made on how the final solution can be selected from the Pareto frontier according to the design objectives. The presented framework can find a set of Pareto optimal solutions as a trade-off between cost and pollution objectives by considering different combinations of electric and combustion vehicles. It was shown that those solutions that involve more electric fleet than combustion fleet, lead to higher total costs and smaller emissions and vice versa.