In this article, we investigate a two-tier delivery network with robots operating on the second tier. We determine the optimal number of local robot hubs as well as the optimal number of robots to service all customers and compare the resulting operational cost to conventional truck-based deliveries. Based on the well-known p-median problem, we present mixed-integer programs that consider the limited range of robots due to battery size. Compared with conventional truck-based deliveries, robot-based deliveries can save about 70% of operational cost and even more, up to 90%, for instances with customer time windows.

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Since delivery robots share sidewalks with pedestrians, it may be beneficial to choose paths for them that avoid zones with high pedestrian density. In this paper, we investigate a robot-based last-mile delivery problem considering path flexibility given the presence of zones with varying pedestrian level of service (LOS). Pedestrian LOS is a measure of pedestrian flow density. We model this new problem with stochastic travel times and soft customer time windows. The model includes an objective that reflects customer service quality based on early and late arrivals. The heuristic solution approach uses the minimum travel time paths from different LOS zones (path flexibility). We demonstrate that the presence of pedestrian zones leads to alternative path choices in 30% of all cases. In addition, we find that extended time windows may help increase service quality in zones with high pedestrian density by up to 40%.

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