The mixed-fleet vehicle routing problem with low emission zones

Many cities initiated new measures to restrict the access of internal combustion engine vehicles (ICEVs) to urban centers because of increasing concerns in societies regarding carbon emissions and noise. A common restriction is referred to as low emission zone (LEZ) where ICEVs are either banned from entering or required to pay a daily toll to enter, whereas green vehicles such as electric vehicles (EVs) are exempt from any access restriction and toll payment. Therefore, delivery companies operating in LEZs face new challenges to determine their fleet configurations and make route plans. In this paper, we tackle this issue by adopting an optimization-based approach, which deals with routing a mixed fleet of vehicles that serves customers located inside and outside the LEZ. The fleet consists of ICEVs and EVs that are allowed to recharge en route. The objective is to minimize total operating costs that comprises the charging cost of EVs, fuel cost of ICEVs, and tolls paid by ICEVs that enter the LEZ. We present the mixed integer linear programming formulation of the problem and use it to solve small-size instances. For solving large-size instances, we develop an Adaptive Large Neighborhood Search method that benefits from new problem-specific mechanisms. An extensive experimental campaign is carried out on a set of benchmark instances derived from the literature and a case study based on real data is provided. Numerical results validate the effectiveness of the proposed method and provide managerial insights.