Innovative Applications of O.R.Scheduling last-mile deliveries with truck-based autonomous robots
Introduction
To attenuate the negative effects of transportation on congestion, safety, and environment in large city centers, plenty of innovative concepts for moving people and freight have recently been developed. Among those concepts, especially focusing on freight transportation, are, for instance, goods distribution with electric vehicles (Pelletier, Jabali, & Laporte, 2016), drone-based freight transport (Murray & Chu, 2015), delivery into the trunk of a parked car (Reyes, Savelsbergh, & Toriello, 2017), and crowdsourcing of deliveries (Arslan, Agatz, Kroon, & Zuidwijk, 2016). An overview of the latest developments and concepts in city logistics is, for instance, provided by Savelsbergh and Van Woensel (2016). The novel concept focused in this paper relies on autonomous robots launched from a truck (see Fig. 1).
In September 2016, German truck producer Mercedes-Benz Vans announced a strategic partnership with Starship Technologies (Daimler, 2017). The latter is an Estonian start-up company which develops autonomous robots for last-mile deliveries. Starship’s robots move along sidewalks and weigh no more than 40 pounds, fully loaded. They can be applied to deliver parcels or groceries directly from stores or specialized hubs. Customers can monitor deliveries via smartphones which are also applied to open the locked cargo bay of the robots upon arrival. Afterwards, the robots autonomously return to their store or hub. Due to safety reasons, the robots are only permitted to move at pedestrian speed, so that either a dense (and costly) network of stores or depots is required or (comparatively) long delivery times have to be accepted. To avoid these drawbacks, the aforementioned alliance advocates a concept where trucks are used as mobile launching platforms for the robots.
The truck-based robot delivery concept works as follows. A truck loads the shipments for a set of customers at a central depot where the goods to be shipped are stored. A fixed part of the truck’s loading capacity is reserved to also load autonomous robots on board. The truck, then, moves into the city center and, once a drop-off point is reached, one or multiple robots are loaded with shipments and launched to autonomously deliver their goods to customers. Each robot has a capacity for a single shipment and after delivery, returns to a decentralized robot depot within the city center. Note that at these decentralized depots, only robots are stored but not goods, so that only a small garage is required but no complete distribution center. The truck moves onwards to successive drop-off points until all robots are released. If the truck still has further shipments for additional customers on board, it can move to one of the decentralized robot depots to load another batch of robots. In this way, the process goes on until all shipments on board of the truck are launched with a robot and the truck can return to the central depot in order to load more shipments for the next set of customers.
This paper introduces scheduling procedures for an efficient truck-based robot delivery. Specifically, we aim at a truck route along a sequence of stops consisting of drop-off points and decentralized robot depots along with a launching plan of robots, such that the weighted number of late customer deliveries, after the announced delivery date, is minimized. This problem is defined, computational complexity is proven, and exact as well as heuristic solution methods are introduced. The devil’s advocate could say that the second problem is treated before the first. First, all technological challenges should be solved and government admission for the robots on public roads should be reached (first problem). Afterwards, there is still enough time to develop suited scheduling procedures (second problem). However, it seems hard to properly anticipate the potential gains of the truck-based robot delivery concept without a detailed scheduling procedure which is able to exactly quantify important performance indicators, such as the resulting travel distances. Therefore, to get a first impression of the efficiency of a truck-based robot delivery, we apply our scheduling procedures to different data sets and benchmark them with traditional attended home delivery by truck. Furthermore, we compare our approach to an alternative process of the truck-based robot delivery concept. Instead of applying decentralized robot depots, the truck could also wait for the return of launched robots. Our computations, however, show that, due to the robots’ low travel speed, this alternative mode of operation is considerably inferior.
The remainder of the paper is structured as follows. A brief literature review is provided in Section 2. Then, Section 3 defines our optimization problem and Section 4 elaborates on suited exact as well as heuristic solution procedures, whose computational performance is tested in Section 5. The comparison of the two alternative modes of operation of truck-based robot deliveries and their benchmarking with conventional attended home deliveries by truck is provided in Section 6. Finally, Section 7 concludes the paper.
Section snippets
Literature review
Several innovative concepts for the transport of people and goods have recently been developed. Instead of trying to summarize the vast body of literature which has accumulated in this area, we refer to the recent survey papers on trends in transportation (Speranza, 2018), distribution with electric vehicles (Pelletier et al., 2016), shared transportation (Miller, 2013), and city logistics (Savelsbergh & Van Woensel, 2016). One of the latest concepts, announced in September 2016 (Daimler, 2017
Problem definition
Consider a single truck loaded with shipments for a set C of customers to be supplied. Initially, the truck is positioned at location γ with δ robots on board. This location may be the central depot where the customers’ shipments are loaded and an initial delivery schedule is determined. In case of unforeseen events, such as congestion, however, a short-term adaption of the initial plan may become necessary, so that γ and δ can also represent the truck’s current status-quo on a half-finished
Solution methods
This section is dedicated to suited solution procedures of our TBRD problem. After presenting a MIP model in Section 4.1, we provide an efficient approach to determine an optimal assignment of customers to drop-off points and robot depots for a predetermined truck route in Section 4.2. Based on this, we introduce a tailor-made local search procedure in Section 4.3.
Performance of algorithms
In this section, we test the performance of our solution methods. Since no established testbed is available for our TBRD, we first elaborate how our instances have been generated (see Section 5.1). Afterwards in Section 5.2, we benchmark the performance results of our heuristic solution procedure with a standard solver solving TBRD-MIP.
All computations have been executed on a 64-bit PC with an Intel Core i7-6700K CPU (4 × 4.0 gigahertz), 64 gigabytes main memory, and Windows 7 Enterprise. The
Managerial aspects
Beyond the pure computational performance, this section is dedicated to managerial aspects. Specifically, we report on the results of a sensitivity analysis in Section 6.1. Here, we explore how the network density of robot depots and drop-off points as well as the velocity of the robots and the truck’s capacity for robots impact the timeliness of deliveries. Furthermore, in Section 6.2 we benchmark our delivery policy where the robots return to decentralized robot depots with two alternative
Conclusion
This paper investigates an innovative last-mile concept where autonomous robots are launched from trucks to deliver shipments towards customers. After delivery, the robots return to decentralized robot depots where a delivery truck can take them on board again. This paper focuses on the scheduling of the delivery truck and the launching of robots along the truck route, such that customers are timely delivered. We formulate the resulting scheduling problem, prove computational complexity, and
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