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We propose a model for optimizing the last-mile delivery of n packages, from a distribution center to their final recipients, using a strategy that combines the use of ride-sharing platforms (e.g., Uber or Lyft) with traditional in-house van delivery systems. The main objective is to compute the optimal reward offered to private drivers for each of the n packages, such that the total expected cost of delivering all packages is minimized. Our technical approach is based on the formulation of a discrete sequential packing problem, where bundles of packages are picked up from the warehouse at random times during the interval [0, T]. Our theoretical results include both exact and asymptotic (as $n to infty$) expressions for the expected number of packages that will be picked up by time T, and are closely related to the classical Renyis parking/packing problem.
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E-commerce has evolved with the digital technology revolution over the years. Last-mile logistics service contributes a significant part of the e-commerce experience. In contrast to the traditional last-mile logistics services, smart logistics service with autonomous driving technologies provides a promising solution to reduce the delivery cost and to improve efficiency. However, the traffic conditions in complex traffic environments, such as those in China, are more challenging compared to those in well-developed countries. Many types of moving objects (such as pedestrians, bicycles, electric bicycles, and motorcycles, etc.) share the road with autonomous vehicles, and their behaviors are not easy to track and predict. This paper introduces a technical solution from JD.com, a leading E-commerce company in China, to the autonomous last-mile delivery in complex traffic environments. Concretely, the methodologies in each module of our autonomous vehicles are presented, together with safety guarantee strategies. Up to this point, JD.com has deployed more than 300 self-driving vehicles for trial operations in tens of provinces of China, with an accumulated 715,819 miles and up to millions of on-road testing hours.
In this paper, we investigate the problem of a last-mile delivery service that selects up to $N$ available vehicles to deliver $M$ packages from a centralized depot to $M$ delivery locations. The objective of the last-mile delivery service is to jointly maximize customer satisfaction (minimize delivery time) and minimize operating cost (minimize total travel time) by selecting the optimal number of vehicles to perform the deliveries. We model this as an assignment (vehicles to packages) and path planning (determining the delivery order and route) problem, which is equivalent to the NP-hard multiple traveling salesperson problem. We propose a scalable heuristic algorithm, which sacrifices some optimality to achieve a reasonable computational cost for a high number of packages. The algorithm combines hierarchical clustering with a greedy search. To validate our approach, we compare the results of our simulation to experiments in a $1$:$25$ scale robotic testbed for future mobility systems.
Parking is a necessary component of traditional last-mile delivery practices, but finding parking can be difficult. Yet, the routing literature largely does not account for the need to find parking. In this paper, we address this challenge of finding parking through the Capacitated Delivery Problem with Parking (CDPP). Unlike other models in the literature, the CDPP accounts for the search time for parking in the objective and minimizes the completion time of the delivery tour. We provide tight bounds for the CDPP using a Traveling Salesman Problem (TSP) solution that parks at each customer. We then demonstrate the circumstances under which this TSP solution is the optimal solution to the CDPP as well as counterexamples to show that the TSP is generally not optimal. We also identify model improvements that allow reasonably-sized instances of the CDPP to be solved exactly. We introduce a heuristic for the CDPP that quickly finds high quality solutions to large instances. Computational experiments show that parking matters in last-mile delivery optimization. The CDPP outperforms industry practice and models in the literature showing the greatest advantage when the search time for parking is high. This analysis provides immediate ways to improve routing in last-mile delivery.
In this work, we study discrete-time Markov decision processes (MDPs) under constraints with Borel state and action spaces and where all the performance functions have the same form of the expected total reward (ETR) criterion over the infinite time horizon. One of our objective is to propose a convex programming formulation for this type of MDPs. It will be shown that the values of the constrained control problem and the associated convex program coincide and that if there exists an optimal solution to the convex program then there exists a stationary randomized policy which is optimal for the MDP. It will be also shown that in the framework of constrained control problems, the supremum of the expected total rewards over the set of randomized policies is equal to the supremum of the expected total rewards over the set of stationary randomized policies. We consider standard hypotheses such as the so-called continuity-compactness conditions and a Slater-type condition. Our assumptions are quite weak to deal with cases that have not yet been addressed in the literature. An example is presented to illustrate our results with respect to those of the literature.
In this paper we develop a unified approach for solving a wide class of sequential selection problems. This class includes, but is not limited to, selection problems with no-information, rank-dependent rewards, and considers both fixed as well as random problem horizons. The proposed framework is based on a reduction of the original selection problem to one of optimal stopping for a sequence of judiciously constructed independent random variables. We demonstrate that our approach allows exact and efficient computation of optimal policies and various performance metrics thereof for a variety of sequential selection problems, several of which have not been solved to date.
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