We propose a model for solving a parcel delivery problem with a fleet of trucks embedded with drones. When appropriate, drones are loaded with a parcel, launched directly from the truck, and sent to a client. Afterward, the drones autonomously return to the truck to be replenished and recharged. Inspired by the case of a large European logistics provider, the proposed modeling framework confronts realistic delivery problems involving time windows, limited drone autonomy, and the eligibility of clients to be served by drones. The considered global cost function includes fixed daily vehicle fares, driver wages, and the fuel and electricity consumption to power trucks and drones. To solve the problems at hand, we propose a mixed-integer linear programming formulation and an adaptive large neighborhood search. Moreover, we introduce an efficient modeling framework to manage the numerous synchronization constraints induced by the simultaneous use of trucks and drones. We analyze the benefits of this new transportation concept for delivery problems involving up to 100 parcels. Results show that truck-and-drone solutions can reduce costs up to 34% compared to traditional truck-only delivery. From a managerial perspective, we show that a certain percentage of client locations must be reachable by drone to make truck-and-drone solutions competitive (i.e., if the fixed costs of the drones are compensated for by the savings on truck routes) and compare the cost structures of truck-and-drone versus truck-only solutions.

中文翻译：

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使用卡车和无人机在时间窗口限制下最小化包裹递送成本

我们提出了一个模型，用于解决一个装有无人机的卡车车队的包裹递送问题。在适当的时候，无人机会装载包裹，直接从卡车上发射，然后发送给客户。之后，无人机自动返回卡车进行补充和充电。受欧洲大型物流供应商案例的启发，提议的建模框架面临着现实的交付问题，包括时间窗口、有限的无人机自主权以及客户接受无人机服务的资格。考虑的全局成本函数包括固定的每日车辆票价、司机工资以及为卡车和无人机提供动力的燃料和电力消耗。为了解决手头的问题，我们提出了混合整数线性规划公式和自适应大邻域搜索。而且，我们引入了一个有效的建模框架来管理由同时使用卡车和无人机引起的众多同步约束。我们分析了这种新运输概念对于涉及多达 100 个包裹的交付问题的好处。结果表明，与传统的仅使用卡车的交付相比，卡车和无人机解决方案可以将成本降低多达 34%。从管理的角度来看，我们表明无人机必须可以到达一定比例的客户位置，以使卡车和无人机解决方案具有竞争力（即，如果无人机的固定成本可以通过卡车路线的节省来补偿），并进行比较卡车和无人机与仅卡车解决方案的成本结构。我们分析了这种新运输概念对于涉及多达 100 个包裹的交付问题的好处。结果表明，与传统的仅使用卡车的交付相比，卡车和无人机解决方案可以将成本降低多达 34%。从管理的角度来看，我们表明无人机必须可以到达一定比例的客户位置，以使卡车和无人机解决方案具有竞争力（即，如果无人机的固定成本可以通过卡车路线的节省来补偿）并比较卡车和无人机与仅卡车解决方案的成本结构。我们分析了这种新运输概念对于涉及多达 100 个包裹的交付问题的好处。结果表明，与传统的仅使用卡车的交付相比，卡车和无人机解决方案可以将成本降低多达 34%。从管理的角度来看，我们表明无人机必须可以到达一定比例的客户位置，以使卡车和无人机解决方案具有竞争力（即，如果无人机的固定成本可以通过卡车路线的节省来补偿）并比较卡车和无人机与仅卡车解决方案的成本结构。