Data-driven optimization of a mixed fleet of drones and human couriers for on-demand delivery under uncertainty

On-demand delivery, which allows consumers to receive purchases quickly after ordering, is becoming increasingly prevalent. While human couriers are commonly used for deliveries, they often lead to higher costs and longer delivery times. Drones can help overcome these limitations but have a shorter range compared to human couriers. Therefore, utilizing a mixed fleet of drones and human couriers offers an effective solution for fast, cost-efficient, and reliable on-demand delivery. This paper focuses on an on-demand delivery system in which a mixed fleet of drones and human couriers collects parcels from a central hub and delivers them to parcel lockers across multiple regions throughout a day, under uncertain parcel demand. We propose a two-stage Wasserstein distributionally robust optimization (DRO) model to jointly optimize the allocation and operation of drones and human couriers in the face of demand uncertainty. We propose reformulation techniques to transform the model into a tractable form. To enhance computational efficiency, we develop an L-shaped algorithm and an alternating direction algorithm. Out-of-sample results based on real-world data highlight the benefits of employing DRO approach. Additionally, we reveal that a mixed fleet outperforms using only drones or only human couriers, with drones prioritized for deliveries and serving as the dominant role, while human couriers play a supplementary role. We also examine how the performance of drones and human couriers varies with changes in several key system parameters.