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

Abstract

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 with bounded makespans 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 accurately approximates the average routing performance and the fleet size required to establish an online food delivery service without the operation details. Using the results, 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. We apply the model to 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.