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Note on the dominance rules in the exact algorithm for the container pre-marshalling problem by Tanaka & Tierney (2018)

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  • Jin, Bo
  • Yu, Mingzhu

Abstract

In this note, we identify an over-pruning issue that occurs in the iterative deepening branch-and-bound algorithm by Tanaka and Tierney (2018). We show that this over-pruning issue is caused by an inconsistency between two dominance rules, namely, the transitive move rule and the empty stack rule, and it will in turn cause the exact algorithm to produce incorrect optimal solutions. To address this issue, we propose a new concept termed the lexicographic dominance principle, and prove that all dominance rules under the lexicographic dominance principle are mutually consistent. Finally, we re-examine all the dominance rules described in the referred paper, and present a compatible set of dominance rules to guarantee mutual consistency.

Suggested Citation

  • Jin, Bo & Yu, Mingzhu, 2021. "Note on the dominance rules in the exact algorithm for the container pre-marshalling problem by Tanaka & Tierney (2018)," European Journal of Operational Research, Elsevier, vol. 293(2), pages 802-807.
    • Handle: RePEc:eee:ejores:v:293:y:2021:i:2:p:802-807
    DOI: 10.1016/j.ejor.2020.12.041
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    References listed on IDEAS

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    1. Tanaka, Shunji & Tierney, Kevin & Parreño-Torres, Consuelo & Alvarez-Valdes, Ramon & Ruiz, Rubén, 2019. "A branch and bound approach for large pre-marshalling problems," European Journal of Operational Research, Elsevier, vol. 278(1), pages 211-225.
    2. Tanaka, Shunji & Voß, Stefan, 2019. "An exact algorithm for the block relocation problem with a stowage plan," European Journal of Operational Research, Elsevier, vol. 279(3), pages 767-781.
    3. Tanaka, Shunji & Tierney, Kevin, 2018. "Solving real-world sized container pre-marshalling problems with an iterative deepening branch-and-bound algorithm," European Journal of Operational Research, Elsevier, vol. 264(1), pages 165-180.
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    Cited by:

    1. 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.

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