In this paper, we are interested in studying the traveling salesman problem with drone (TSP‐D). Given a set of customers and a truck that is equipped with a single drone, the TSP‐D asks that all customers are served exactly once and minimal delivery time is achieved. We provide two compact mixed integer linear programming formulations that can be used to address instances with up to 10 customer within a few seconds. Notably, we introduce a third formulation for the TSP‐D with an exponential number of constraints. The latter formulation is suitable to be solved by a branch‐and‐cut algorithm. Indeed, this approach can be used to find optimal solutions for several instances with up to 20 customers within 1 hour, thus challenging the current state‐of‐the‐art in solving the TSP‐D. A detailed numerical study provides an in‐depth comparison on the effectiveness of the proposed formulations. Moreover, we reveal further details on the operational characteristics of a drone‐assisted delivery system. By using three different sets of benchmark instances, consideration is given to various assumptions that affect, for example, technological drone parameters and the impact of distance metrics.

中文翻译：

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无人机行销业务员问题的分支方法和替代公式

在本文中，我们有兴趣研究无人机的旅行推销员问题（TSP-D）。对于给定的一组客户和配备一架无人驾驶飞机的卡车，TSP-D要求为所有客户提供准确的服务一次，并缩短交货时间。我们提供两种紧凑的混合整数线性规划公式，可用于在几秒钟内解决多达10个客户的实例。值得注意的是，我们为TSP-D引入了第三种形式，其约束数量呈指数级增长。后一种公式适合用分支剪切算法求解。实际上，这种方法可用于在1小时内为多达20个客户的多个实例找到最佳解决方案，从而在解决TSP-D方面挑战了当前的最新技术。详尽的数值研究提供了对所提出配方的有效性的深入比较。此外，我们将揭示有关无人机辅助传送系统的操作特性的更多细节。通过使用三组不同的基准实例，可以考虑影响例如技术无人机参数和距离度量标准影响的各种假设。