Dynamic Switching Models for Truck-only Delivery and Drone-assisted Truck Delivery under Demand Uncertainty

Integrating drones into truck delivery systems can improve customer accessibility, reduce operational costs, and increase delivery efficiency. However, drone deployment incurs costs, including procurement, maintenance, and energy consumption, and its benefits depend on service demand. In low-demand areas, drone-assisted trucks may underutilize resources due to high upfront costs. Accurately predicting demand is challenging due to uncertainties from unforeseen events or infrastructure disruptions. To address this, a market entry and exit real option approach is used to optimize switching between truck-only and drone-assisted delivery under stochastic demand. Results show that deploying multiple drones per truck offers significant cost advantages in high-demand regions. Using the proposed dynamic switching model, deterministic and stochastic approaches reduce costs by 17.4% and 31.3%, respectively, compared to immediate cost-saving switching. Sensitivity analysis reveals asymmetric effects of stochastic parameters on entry and exit timings. A stochastic multiple-options model is further developed to dynamically switch between truck-only and drone-assisted delivery with varying drone numbers. Applying these models to Miami-Dade County, we evaluate dynamic switching costs for three major logistics operators. This study highlights the potential benefits of dynamic delivery switching and provides insights for optimizing logistics operations.