Approximate dynamic programming for container stacking - Boschma, René; Mes, Martijn R.K.; de Vries, Leon R. (European journal of operational research, 2023)
•Novel approach to minimize reshuffles at container terminals.•Extensions of the Container Relocation Problem and Block Relocation Problem.•Consideration of uncertainty in arrival times of both in- and outbound containers.•Approximate Dynamic Programming approach to support realtime decision making.•Validation of the approach using real-life container terminals. At some point during transport, intermodal containers will be stored at a terminal, where they are typically stacked on top of each other. Stacking yields a higher utilization of the area but may lead to unproductive reshuffle moves when containers below another need to be retrieved. Preventing reshuffles has a financial benefit, as it not only avoids the costs of executing the reshuffle but also decreases the time needed to retrieve a container. Typically, researchers consider only the retrieval of containers and assume the retrieval order is fully known. In addition, existing studies do not consider the stacking restrictions imposed by a reach stacker, which is commonly used in smaller inland terminals. This research aims to design decision support for determining real-life applicable container stack allocations so that the expected number of reshuffles is minimized. We propose a model that includes both arrivals and departures of containers as well as a certain level of uncertainty in the order thereof. The problem is modeled as a Markov Decision Process and solved using Approximate Dynamic Programming (ADP). Through numerical experiments on real-life problem instances, we conclude that the ADP approach drastically outperforms a benchmark heuristic from the literature. All data used as well as the source code has been made publicly available.