Summary: The spread of COVID-19 outbreak has promoted truck-drone delivery from trials to commercial applications in end-to-end contactless solutions. To fully integrate truck-drone delivery in contactless solutions, we introduce the robust traveling salesman problem with a drone, in which a drone makes deliveries and returns to the truck that is moving on its route under uncertainty. The challenge is to find, for each customer location in truck-drone routing, an assignment to minimize the expected makespan. Apart from the complexity of this problem, the risk of synchronization failure associated with uncertain travel time should be also considered. The problem is first formulated as a robust model, and a novel efficient frontier heuristic is proposed to solve this model. By coupling the implicit adaptive weighting with epsilon-constraint methods, the heuristic generates a series of scalarized single-objective problems, where the goal is to minimize expected makespan under the constraint of synchronization risk. The experiment results show that the robust (near-)optimal solutions offer a considerable reduction in risk, yet only hint at a small increase in makespan. The heuristic in the present study is effective to construct approximations of Pareto frontier and allows for assignment decisions in a priori or a posteriori manner.
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