The Delivery Dispatching Problem with Time Windows for Urban Consolidation Centers

Abstract

This paper addresses the dispatch decision problem faced by an urban consolidation center. The center receives orders according to a stochastic arrival process, and dispatches them for the last-mile distribution in batches. The operator of the center aims to find the cost-minimizing consolidation policy, depending on the orders at hand, pre-announced orders, and stochastic arrivals. We present this problem as a variant of the Delivery Dispatching Problem that includes dispatch windows, and model it as a Markov decision problem. For toy-sized instances, we solve this model to optimality. Through numerical experiments on these instances, we show that we approximate the optimal values with an error of less than 2%. Larger instances suffer from intractably large state-, outcome-, and action spaces. We propose an Approximate Dynamic Programming (ADP) algorithm that can handle such instances, using value function approximation to estimate the downstream costs. To cope with large action spaces -with sizes up to 2 120 in our experiments -we formulate an integer linear program to be used within our ADP algorithm. To evaluate the performance of our ADP policies, we test against various benchmark policies, including a lookahead policy based on scenario sampling. We test the performance of ADP on a variety of networks. When the dispatching problem provides sufficient flexibility in dispatch times, ADP outperforms our myopic benchmark policies by more than 15%, and lookahead policies by over 10%. * Corresponding author. Address:

Comparison of Manual and Automated Decision-Making with a Logistics Serious Game

“…Many variants of the DDP exist; we build upon the variant presented by Pérez Rivera & Mes [9], involving a barge that can carry multiple containers and trucks that serve as alternative transport modality. For closely related DDP variants, Pérez Rivera & Mes [10] and Van Heeswijk et al [14] present several baseline heuristics composed of simple decision rules that achieve consolidation, yet these heuristics ignore various considerations that humans would intuitively make. The aforementioned papers also develop VFA-based RL algorithms, testing a variety of attribute designs.…”

A State Aggregation Approach for Stochastic Multiperiod Last-Mile Ride-Sharing Problems

“…Compared to this line of work, our formulation can be seen as an extension, as we explicitly consider the vehicle routing element, instead of using close-form approximations. A similar effort has been made by van Heeswijk et al (2017) to explicitly incorporate the routing problem in the DDP formulation. Compared to this latest work, our formulation is different in that we adopt infinite planning horizon and utilize an ADP approach that does not depend on the basis function.…”

Scalability and Performance of Decentralized Planning in Flexible Transport Networks

“…In stochastic and dynamic settings, scenario sampling or value function approximation (which true value depends on the underlying stochastic process) are the most common solution methods [3]. Examples of both approaches may be found in Lium et al [4] and Van Heeswijk et al [5], respectively.…”

“…The fourth policy (π 4 ) estimates downstream costs corresponding to each action based on sampling future states and solving them with π 2 . The seminal work of Bertsekas [9] refers to this widely accepted method as a rollout algorithm and is known to be competitive to value function approximation [11,5].…”

“…Performance per policy for each instance. Centralized policy π c cannot be computed within time for the instances 10(4) and 25(5).…”