The flying sidekick traveling salesman problem (FS-TSP) is a parcel delivery problem arising in the last-mile logistics, where the distribution plan of a driver-operated truck assisted by a drone (unmanned aerial vehicle, UAV) has to be defined. The FS-TSP is a variant of the TSP where routing decisions are integrated with customer-to-drone and customer-to-truck assignment decisions and truck-and-drone synchronization constraints. The objective is the minimization of the time required to serve all the customers, taking into account drone payload capacity and battery power constraints. In this work we provide a new representation of the FS-TSP based on the definition of an extended graph. This representation allows to model the problem by a new and compact integer linear programming formulation, where the synchronization issue is tackled in a column generation fashion, thus avoiding the usage of big-M constraints, representing one of the main drawbacks of the models present in literature. The proposed formulation has been solved by an exact approach which combines a Branch-and-Cut algorithm and a column generation procedure, strengthened by variable fixing strategies and new valid inequalities specifically defined for the problem. The proposed method has been experienced on a large set of benchmark instances. Computational results show that the proposed approach either is competitive or outperforms the best exact approach present in literature for the FS-TSP. Indeed, it is able to provide the optimal solution for all small size instances with 10 customers and for several medium size instances with 20 customers, some of them never solved before.

飞行搭档旅行业务员问题（FS-TSP）是在最后一英里物流中出现的包裹交付问题，在此问题中，必须定义由无人机（无人驾驶飞机，UAV）辅助的驾驶员操作卡车的分配计划。在FS-TSP是的变体TSP其中的路由决策都集成了客户对无人机和客户到卡车分配决策和卡车和无人机同步约束。目标是将无人机的有效负载容量和电池功率限制因素考虑在内，以最大限度地缩短服务所有客户所需的时间。在这项工作中，我们提供了FS-TSP的新表示形式基于扩展图的定义。此表示允许通过新的紧凑型整数线性规划公式对问题进行建模，其中以列生成方式解决同步问题，从而避免了使用big-M约束，代表了文献中存在的模型的主要缺点之一。所提出的公式已通过精确的方法解决，该方法结合了分支剪切算法和列生成程序，并通过变量固定策略和针对该问题专门定义的新有效不等式得到了加强。所提出的方法已经在大量基准实例上经历过。计算结果表明，所提出的方法具有竞争力，或者优于文献中针对FS-TSP的最佳精确方法。确实，它能够为拥有10个客户的所有小型实例和拥有20个客户的几个中型实例提供最佳解决方案，其中一些以前从未解决过。