Analytical model for large-scale design of sidewalk delivery robot systems

With the rise in demand for local deliveries and e-commerce, robotic deliveries are being considered as efficient and sustainable solutions. However, the deployment of such systems can be highly complex due to numerous factors involving stochastic demand, stochastic charging and maintenance needs, complex routing, etc. We propose a model that uses continuous approximation methods for evaluating service trade-offs that consider the unique characteristics of large-scale sidewalk delivery robot systems used to serve online food deliveries. The model captures both the initial cost and the operation cost of the delivery system and evaluates the impact of constraints and operation strategies on the deployment. By minimizing the system cost, variables related to the system design can be determined. First, the minimization problem is formulated based on a homogeneous area, and the optimal system cost can be derived as a closed-form expression. By evaluating the expression, relationships between variables and the system cost can be directly obtained. We then apply the model in neighborhoods in New York City to evaluate the cost of deploying the sidewalk delivery robot system in a real-world scenario. The results shed light on the potential of deploying such a system in the future.