This paper introduces the Energy Minimizing and Range Constrained Drone Delivery Problem (ERDDP) in which drones are used to make deliveries to a number of customers and the drones themselves are transported by traditional vehicles that act as launch points. The ERDDP consists of (i) selecting the launch points from a potential set of sites from where drones will take off to serve a number of customers, (ii) assignments of customers to the launch points, and (iii) the speed at which drones are to travel between the customers and the launch points. The paper presents a nonlinear model for the ERDDP, which minimizes the total operational cost including an explicit calculation of the energy consumption of the drone as a function of the drone speed. The deliveries are limited by both a service time bound and the range of the drone. The model is reformulated using second order cone programming, and subsequently strengthened by the use of perspective cuts, that allows the use of off-the-shelf optimization software to solve the problem. Computational results are presented on a realistic data set that quantifies the effect of various parameters on location, assignment and speed decisions.

本文介绍了能量最小化和射程受限的无人机交付问题（ERDDP），其中使用无人机向许多客户进行交付，而无人机本身则通过充当发射点的传统车辆进行运输。ERDDP包括（i）从可能从无人机起飞的站点中选择发射点，以为许多客户提供服务；（ii）将客户分配给发射点；以及（iii）无人机的速度在客户和发射点之间旅行。本文提出了一种用于ERDDP的非线性模型，该模型可以最大程度地降低总运营成本，其中包括根据无人机速度显式计算无人机能耗。交付受到服务时间限制和无人机范围的限制。该模型使用二阶锥规划进行了重新编制，随后通过使用透视切口进行了增强，从而可以使用现有的优化软件来解决该问题。计算结果显示在现实的数据集上，该数据集量化了各种参数对位置，分配和速度决策的影响。