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•We propose a integrated scheme for instant delivery with vehicles and UAVs.•We formulate two models with hierarchy and back propagation for the scheme.•We introduce two improved ant colony algorithms for the scheme.
Instant delivery by ground vehicles combined with unmanned aerial vehicles (UAVs) will greatly expand its coverage range while expanding its application. In this paper, a novel operation scheme with vehicles and UAVs for instant delivery is presented. This scheme consists of four key processes: the locations of vehicle stops, the allocation of customers to vehicle stops, the allocation of customers to UAVs, and route planning for vehicles. We formulate a capacitated set covering location model to determine the number and feasible locations of vehicle stops. Moreover, we present a multilevel model to optimize the decisions on the remaining processes and finally determine the locations of vehicle stops while minimizing the number of vehicles dispatched and the total travel time. Furthermore, we propose two advanced ant colony optimization (ACO) by introducing variable visibility and multilevel feedback pheromones. Experiments are applied to prove the effectiveness of the operation scheme with vehicles and UAVs.