Comparison of compact formulations for the electric vehicle routing problem

The electric vehicle routing problem is an extension of the capacitated vehicle routing problem, where en-route recharging needs to be addressed due to the limited driving range of electric vehicles. In this study, we compare four compact formulations that differ in the way they model the battery consumption. The first two formulations use Miller–Tucker–Zemlin’s approach, while the last two use single-commodity flows for this purpose. Within each approach, the two formulations have distinct ways of dealing with the fact that recharging stations may be visited more than once. In particular, two formulations make use of arcs that correspond to two-leg paths with a recharging station in the middle, whereas the other two formulations use copies of recharging stations, as suggested in the literature. We compare the linear programming bounds of these four formulations as well as the existing formulations from a theoretical point of view. Then, we analyze the performance of the new and existing formulations using six sets of benchmark instances. The computational results show that our formulations tighten the linear programming bounds and require less computation time to prove optimality.