The green vehicle routing problem with non-linear charging functions

The use of EVs leads to new optimization problems. One of them is the green vehicle routing problem (Green VRP). The Green VRP is an extension of the well-known vehicle routing problem, arising when a fleet of zero emission vehicles (ZEV) based at a central depot services a set of geographically spread customers. The special feature of this VRP comes from the limited range of ZEVs. To ensure the feasible completion of trips, the ZEVs may visit alternative fuel stations en-route to refill the tank or recharge the battery. Most of the research carried on the Green VRP relies on the assumption that the tank or the battery is always recharge up to its maximum capacity. Nonetheless, in practice the portion of the tank or battery to charge is a decision variable. In this study we introduce the green vehicle routing problem with non-linear charging function (Green VRP-NLCF), that includes the charging quantity as a decision, with nonlinear charging behaviour. We propose a mixed-integer linear programming (MILP) formulation and a two-phase heuristic.