The traveling salesman problem with drone based on vehicle mobile parking for customer self-pickup

This paper introduces the traveling salesman problem with drone based on vehicle mobile parking for customer self-pickup (TSPD-VMPCP) in last-mile delivery. A set of vertices is considered, including a depot, parking spots, home delivery (HD) customers that must be visited directly within predefined time windows by truck or drone, and customers with self-pickup (CP) preference that must be served by designated parking spots. Specifically, we allow the drone to perform multi-loop, in which the drone launches and lands at the same location. CP customers are covered using a probability function based on their self-pickup behavior and the truck's stoppage duration. The TSPD-VMPCP aims to minimize the total operating cost. We model the TSPD-VMPCP as a mixed-integer linear program and develop an adaptive large neighborhood search (ALNS) metaheuristic, in addition to a two-phase local search (2P-LS) based on variable neighborhood descent (VND) and matheuristic. We assess the performance of ALNS by comparing it with the Gurobi solver on small instances. The numerical results for medium and large instances highlight the effectiveness of the various components of the ALNS. Furthermore, we provide some managerial insights.