Managing price and fleet size for courier service with shared drones

•The drone delivery service system is formulated as a time-varying, and price sensitive queueing model.•A stochastic control model is formulated to maximize the profit for the platform with the QoS (quality of service) constraints.•A fluid control model is applied to simplify the stochastic control problem, and a closed-form pricing function is obtained.•A numerical method is proposed to handle the approximation under high QoS target.•Simulation analysis is performed to validate the proposed algorithms, which could yield high quality approximations, and the in-control stabilization for key performances. With the rapid development of modern logistics systems, the unmanned aerial vehicle (a.k.a. drone) based delivery service emerges as a technology-driven innovation, and it is now pilot running in many regions across the globe. The drone delivery system aims to reduce the labor cost in the current labor-intensive courier industry, as well as avoid the disturbance caused by geographic and demographic features. For the drone delivery service providers to survive and prosper, a pool of shared drones is integrated into the ecological chain, where the courier service providers focus on the delivery operations. For such a drone sharing system, revenue management becomes vital in terms of pricing, drone hiring cost, and service-related cost. To better depict the system dynamics, in the present paper, a time-varying and price-sensitive queueing model is formulated, where the customer behaviors are taken into account, such as balking and abandonment. To guarantee a preset service level, the probability of abandonment and expected delay are considered as the control targets, and the pricing for courier service and the maintained fleet size are considered simultaneously. For the low and moderate quality of service(QoS) target, a fluid control model is constructed with a closed-form solution. For the high QoS target, a modified approximation algorithm is designed to numerically tackle the problem. Based on the simulation, it is observed that the proposed approximation methods not only provide a high-quality joint strategy but also help stabilize the system performance. In addition, only mild price change is needed to reach the optimal condition, and a time lag exists between the optimal fleet sizing and the demand variation, which may shed light on the demand-driven fleet sizing under more general settings.