With growing consumer demand and expectations, companies are attempting to achieve cost-efficient and faster delivery operations. The integration of autonomous vehicles, such as drones, in the last-mile network design can curtail many operational challenges and provide a competitive advantage. This paper deals with the problem of delivering orders to a set of customer locations using multiple drones that operate in conjunction with a single truck. To take advantage of the drone fleet, the delivery tasks are parallelized by concurrently dispatching the drones from a truck parked at a focal point (ideal drone launch location) to the nearby customer locations. Hence, the key decisions to be optimized are the partitioning of delivery locations into small clusters, identifying a focal point per cluster, and routing the truck through all focal points such that the customer orders in each cluster are fulfilled either by a drone or truck. In contrast to prior studies that tackle this problem using multi-phase sequential procedures, this paper presents mathematical programming models to jointly optimize all the decisions involved. We also consider two polices for choosing a cluster focal point - (i) restricting it to one of the customer locations, and (ii) allowing it to be anywhere in the delivery area (i.e., a customer or non-customer location). Since the models considering unrestricted focal points are computationally expensive, an unsupervised machine learning-based heuristic algorithm is proposed to accelerate the solution time. Initially, we treat the problem as a single objective by independently minimizing either the total cost or delivery completion time. Subsequently, the two conflicting objectives are considered together for obtaining the set of best trade-off solutions. An extensive computational study is conducted to investigate the impacts of restricting the focal points, and the influence of adopting a joint optimization method instead of a sequential approach. Finally, several key insights are obtained to aid the logistics practitioners in decision making.

随着消费者需求和期望的不断增长，公司正在努力实现具有成本效益和更快的交付操作。在最后一英里的网络设计中，将无人驾驶汽车（如无人机）集成到一起可以减少许多运营挑战并提供竞争优势。本文讨论了使用与单个卡车配合操作的多架无人机向一组客户地点交付订单的问题。为了利用无人机机群的优势，通过将无人机从协调中心（理想的无人机发射地点）停放的卡车同时调度到附近的客户地点，来并行化交付任务。因此，要优化的关键决策是将交货地点划分为多个小集群，确定每个集群的焦点，并通过所有联络点安排卡车路线，以使无人驾驶飞机或卡车都能满足每个集群中的客户订单。与使用多阶段顺序过程解决该问题的现有研究相比，本文提出了数学编程模型来共同优化所有涉及的决策。我们还考虑了两个选择群集焦点的策略-（i）将其限制在客户位置之一，以及（ii）允许其位于交付区域中的任何位置（即客户或非客户位置）。由于考虑无限制焦点的模型的计算量很大，因此提出了一种基于无监督机器学习的启发式算法来加快求解时间。原来，我们通过独立地最小化总成本或交付完成时间来将问题视为一个目标。随后，将两个相互矛盾的目标一起考虑以获得最佳的权衡解决方案。进行了广泛的计算研究，以研究限制焦点的影响，以及采用联合优化方法而不是顺序方法的影响。最后，获得了一些关键的见解，以帮助物流从业人员进行决策。以及采用联合优化方法而不是顺序方法的影响。最后，获得了一些关键的见解，以帮助物流从业人员进行决策。以及采用联合优化方法而不是顺序方法的影响。最后，获得了一些关键的见解，以帮助物流从业人员进行决策。