On the Modeling of Recharging Stops in Context of Vehicle Routing Problems

Abstract

Caused by regulations regarding to climate protection, battery electric vehicles (BEVs) offer great opportunities in context of ecological compatibility of urban transport systems. Therefore, operating models in context of vehicle routing are required. Because of the BEVs more restrictive driving range in comparison to vehicles with an internal combustion engine (ICE) and due to the fact of a less-developed network of service stations, model formulations have to include the possibility of recharging at dedicated locations. So additional restrictions in formulations are needed to handle the maximum range depending on battery capacity. There were published only a small number of articles addressed to energy consumption, battery range and possible recharging stops in mixed-integer programming (MIP) formulations in the underlying practice relevant Vehicle Routing Problem with Time Windows (VRPTW) over the past few years. So we describe different MIP-formulations for an enhanced VRPTW, considering capacity restrictions concerning to cargo and energy, customer time windows and the capability of charging stops. Effects of these formulations are shown for small-sized problems, while a column generation approach is presented for more realistic problem instances.