Arc Routing with Electric Vehicles

Concerns about greenhouse gas emissions and government regulations foster the use of electric vehicles. Several recently published articles study the use of electric vehicles (EVs) in node-routing problems. In contrast, this article considers EVs in the context of arc routing while also addressing practically relevant aspects that have not been addressed sufficiently so far. These include dynamic charging of EVs while driving, speed-dependent energy consumption, and non-linear charging functions that depend on the battery state-of-charge and the charging time. A generic way of dealing with these aspects is introduced through the concept of an energy-indexed graph which is used to derive an integer linear programming formulation and an exact solution framework based on branch-and-cut. Efficient construction heuristics and a local search for approximately solving large-scale instances are proposed. These heuristics build upon two different solution encodings for which labeling algorithms for decoding are introduced. A computational study is performed on realistic problem instances. Besides analyzing the performance of all proposed methods, the obtained results provide insights and recommendations on strategic decisions related to the size of the vehicle fleet, the battery size, and the amount of charging facilities.