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Tree search for the stacking problem

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  • Rui Rei
  • João Pedroso

Abstract

The stacking problem is a hard combinatorial optimization problem with high practical interest in, for example, steel storage or container port operations. In this problem, a set of items is stored in a warehouse for a period of time, and a crane is used to place them in a limited number of stacks. Since the entrance and exit of items occurs in an arbitrary order, items may have to be relocated in order to reach and deliver other items below them. The objective of the problem is to find a feasible sequence of movements that delivers all items, while minimizing the total number of movements. We study the scalability of an exact approach to this problem, and propose two heuristic methods to solve it approximately. The two heuristic approaches are a multiple simulation algorithm using semi-greedy construction heuristics, and a stochastic best-first tree search algorithm. The two methods are compared in a set of challenging instances, revealing a superior performance of the tree search approach in most cases. Copyright Springer Science+Business Media, LLC 2013

Suggested Citation

  • Rui Rei & João Pedroso, 2013. "Tree search for the stacking problem," Annals of Operations Research, Springer, vol. 203(1), pages 371-388, March.
    • Handle: RePEc:spr:annopr:v:203:y:2013:i:1:p:371-388:10.1007/s10479-012-1186-2
    DOI: 10.1007/s10479-012-1186-2
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    References listed on IDEAS

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    1. Pedroso, João Pedro & Kubo, Mikio, 2010. "Heuristics and exact methods for number partitioning," European Journal of Operational Research, Elsevier, vol. 202(1), pages 73-81, April.
    2. Mordecai Avriel & Michal Penn & Naomi Shpirer & Smadar Witteboon, 1998. "Stowage planning for container ships to reduce the number of shifts," Annals of Operations Research, Springer, vol. 76(0), pages 55-71, January.
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    Cited by:

    1. Liu, Weimiao & Deng, Tianhu & Li, Jianbin, 2019. "Product packing and stacking under uncertainty: A robust approach," European Journal of Operational Research, Elsevier, vol. 277(3), pages 903-917.
    2. Lehnfeld, Jana & Knust, Sigrid, 2014. "Loading, unloading and premarshalling of stacks in storage areas: Survey and classification," European Journal of Operational Research, Elsevier, vol. 239(2), pages 297-312.
    3. Jin, Bo & Tanaka, Shunji, 2023. "An exact algorithm for the unrestricted container relocation problem with new lower bounds and dominance rules," European Journal of Operational Research, Elsevier, vol. 304(2), pages 494-514.
    4. Galle, Virgile & Barnhart, Cynthia & Jaillet, Patrick, 2018. "Yard Crane Scheduling for container storage, retrieval, and relocation," European Journal of Operational Research, Elsevier, vol. 271(1), pages 288-316.
    5. Martin Olsen & Lars Nørvang Andersen & Allan Gross, 2023. "An asymptotically optimal algorithm for online stacking," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 97(2), pages 161-178, April.
    6. Raeesi, Ramin & Sahebjamnia, Navid & Mansouri, S. Afshin, 2023. "The synergistic effect of operational research and big data analytics in greening container terminal operations: A review and future directions," European Journal of Operational Research, Elsevier, vol. 310(3), pages 943-973.

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