Joint optimization of customer location clustering and drone-based routing for last-mile deliveries

Abstract 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.