The vehicle routing problem with underground logistics: Formulation and algorithm

Recognizing the pressure on urban logistics and the overcapacity of urban public transportation systems during off-peak hours, this study investigates a subway-assisted delivery model. This is a system in which part of the goods to be delivered into a city can be transferred to specific subway stations in advance (e.g., during the night) using underground logistics. During the day, vehicles can then be replenished at these subway stations. In our study, we investigate how a system of this kind affects the decisions to be made by a logistics service provider. We introduce the vehicle routing problem with underground logistics to model how to find the best vehicle routes and goods transfer plan in this system. First, we formulate this problem as a mixed integer linear model. Then, we propose a problem-customized adaptive large neighborhood search heuristic algorithm to solve it. Numerical experiments demonstrate that our methodology performs well in terms of effectiveness and efficiency. Additionally, we discuss the resulting schedules and include a sensitivity analysis of the transfer prices to provide information that can be used in strategic and tactical decision making in a subway-assisted delivery system.