Multi-commodity vehicle-drone routing problem with simultaneous delivery and pickup in humanitarian logistics

We address a novel vehicle-drone routing problem involving multiple categories of relief commodities in the context of humanitarian logistics. Unlike existing studies, the transfer and redistribution of relief commodities from one affected area to other affected areas is allowed. A set of homogeneous vehicle-drone tandems, where each vehicle is paired with a dedicated drone, is exploited to cooperatively perform the pickup and delivery services to minimise an optimality criterion that simultaneously involves cost-effectiveness, delivery timeliness, and delivery equity. To solve the problem, we propose a tailored adaptive large neighbourhood search with deep Q-network (ALNS-DQN) algorithm, where some structural properties-related removal and insertion operator pairs are introduced to enhance the exploration of the solution space. A DQN algorithm is developed to learn how to select suitable removal and insertion operator pairs, and some local search operators are explored to further improve the obtained solutions. Extensive numerical experiments demonstrate the superior performance and adaptability of the proposed ALNS-DQN algorithm compared with two benchmarks, highlighting the superiority of the vehicle-drone transport pattern over the vehicle/helicopter-only transport pattern, as well as the advantages of allowing commodity transfer and redistribution among affected areas.