Approximate dynamic programming for container stacking

René Boschma, Martijn R.K. Mes*, Leon R. de Vries

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

1 Citation (Scopus)
36 Downloads (Pure)


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.

Original languageEnglish
Pages (from-to)328-342
JournalEuropean journal of operational research
Issue number1
Early online date26 Feb 2023
Publication statusPublished - Oct 2023


  • Approximate dynamic programming
  • Container relocation problem
  • Container stacking
  • Intermodal transport
  • OR In maritime industry
  • UT-Hybrid-D


Dive into the research topics of 'Approximate dynamic programming for container stacking'. Together they form a unique fingerprint.

Cite this