
In addition, it is estimated that compared to conventional truck-based deliveries, robot-based deliveries can save up to 90 % of operational costs when they are used in a two-tier structure where trucks consolidate packages and deliver them to local robot hubs, where robots undertake the last-mile delivery ( Bakach et al., 2021). Equipped with GPS, cameras, and several other detectors, a robot can operate in an autonomous manner with potentially just one person supervising up to a hundred of them ( Sulleyman, 2017). The robot moves on the sidewalk at pedestrian speed. It is common that these delivery robots transport exactly one package to a single customer within a pre-specified time window. Several companies like Starship (2020), Robby (2020), and Marble (2020) have developed their own versions of delivery robots, which are currently evaluated in field tests. In contrast to the above options, the deployment of ground robots seems to be an appealing and promising mode of parcel transportation for last-mile deliveries in the near future. In addition, there is a number of privacy concerns regarding drone operations ( Rice, 2019). Furthermore, in the US, the FAA requires an operator to keep a drone within eye shot while operating and prohibits operating more than one drone at a time by one operator ( FAA, 2018). For drone-based deliveries, it has been found that drone noise is more annoying to people than noise emission by vehicles ( Christian and Cabell, 2017). For instance, a wide implementation of electric autonomous vehicles would require substantial investments in the road infrastructure to enable traffic management and coordination ( Hussain and Zeadally, 2018). Some of these solutions are easier to implement than the others. These solutions include, but are not limited to, cargo bikes, self-service parcel lockers, aerial drones, ground based autonomous delivery robots, crowd shipping, and collection-and-delivery points ( Boysen et al., 2020 Janjevic et al., 2019). Given these factors, many logistics service providers are exploring alternative solutions for last-mile deliveries. With the spread of COVID−19, demand for last-mile delivery services has increased even further.
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In addition, the rapid growth of e-commerce has increased the demand for delivery drivers ( Sasso, 2018) and resulted in driver shortages. Partially, this is due to the number of failed deliveries, which leads to additional delivery attempts and increased costs. It is estimated that the last mile constitutes about half of all logistics costs for service providers ( McKinsey and Company, 2016). There are many challenges associated with last-mile delivery, the final step in the retail supply chain.
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In addition, we find that extended time windows may help increase service quality in zones with high pedestrian density by up to 40%. We demonstrate that the presence of pedestrian zones leads to alternative path choices in 30% of all cases. The heuristic solution approach uses the minimum travel time paths from different LOS zones (path flexibility). The model includes an objective that reflects customer service quality based on early and late arrivals.

We model this new problem with stochastic travel times and soft customer time windows. Pedestrian LOS is a measure of pedestrian flow 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). Since delivery robots share sidewalks with pedestrians, it may be beneficial to choose paths for them that avoid zones with high pedestrian density. 3Department of Business Decisions and Analytics, University of Vienna, Vienna, Austria.2Business Analytics Department, Tippie College of Business, University of Iowa, Iowa City, IA, United States.1Mathematics Department, The University of Iowa, Iowa City, IA, United States.Iurii Bakach 1, Ann Melissa Campbell 2 and Jan Fabian Ehmke 3*
