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Robust optimization for premarshalling with uncertain priority classes

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  • Boge, Sven
  • Goerigk, Marc
  • Knust, Sigrid

Abstract

In this paper, we consider the premarshalling problem, where items in a storage area have to be sorted for convenient retrieval. A new model for uncertainty is introduced, where the priority values induced by the retrieval sequence of the items are uncertain. We develop a robust optimization approach for this setting, study complexity issues, and provide different mixed-integer programming formulations. In a computational study using a wide range of benchmark instances from the literature, we investigate both the efficiency of the approach as well as the benefit and cost of robust solutions. We find that it is possible to achieve a considerably improved level of robustness by using just a few additional relocations in comparison to solutions which do not take uncertainty into account.

Suggested Citation

  • Boge, Sven & Goerigk, Marc & Knust, Sigrid, 2020. "Robust optimization for premarshalling with uncertain priority classes," European Journal of Operational Research, Elsevier, vol. 287(1), pages 191-210.
    • Handle: RePEc:eee:ejores:v:287:y:2020:i:1:p:191-210
    DOI: 10.1016/j.ejor.2020.04.049
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    References listed on IDEAS

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    1. Parreño-Torres, Consuelo & Alvarez-Valdes, Ramon & Ruiz, Rubén, 2019. "Integer programming models for the pre-marshalling problem," European Journal of Operational Research, Elsevier, vol. 274(1), pages 142-154.
    2. Petering, Matthew E.H. & Hussein, Mazen I., 2013. "A new mixed integer program and extended look-ahead heuristic algorithm for the block relocation problem," European Journal of Operational Research, Elsevier, vol. 231(1), pages 120-130.
    3. Boge, Sven & Knust, Sigrid, 2020. "The parallel stack loading problem minimizing the number of reshuffles in the retrieval stage," European Journal of Operational Research, Elsevier, vol. 280(3), pages 940-952.
    4. 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.
    5. Caserta, Marco & Schwarze, Silvia & Voß, Stefan, 2012. "A mathematical formulation and complexity considerations for the blocks relocation problem," European Journal of Operational Research, Elsevier, vol. 219(1), pages 96-104.
    6. Raka Jovanovic & Milan Tuba & Stefan Voß, 2017. "A multi-heuristic approach for solving the pre-marshalling problem," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 25(1), pages 1-28, March.
    7. Gabrel, Virginie & Murat, Cécile & Thiele, Aurélie, 2014. "Recent advances in robust optimization: An overview," European Journal of Operational Research, Elsevier, vol. 235(3), pages 471-483.
    8. Wang, Ning & Jin, Bo & Zhang, Zizhen & Lim, Andrew, 2017. "A feasibility-based heuristic for the container pre-marshalling problem," European Journal of Operational Research, Elsevier, vol. 256(1), pages 90-101.
    9. Jin, Bo & Zhu, Wenbin & Lim, Andrew, 2015. "Solving the container relocation problem by an improved greedy look-ahead heuristic," European Journal of Operational Research, Elsevier, vol. 240(3), pages 837-847.
    10. Kevin Tierney & Dario Pacino & Stefan Voß, 2017. "Solving the pre-marshalling problem to optimality with A* and IDA," Flexible Services and Manufacturing Journal, Springer, vol. 29(2), pages 223-259, June.
    11. 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.
    12. Bortfeldt, Andreas & Forster, Florian, 2012. "A tree search procedure for the container pre-marshalling problem," European Journal of Operational Research, Elsevier, vol. 217(3), pages 531-540.
    13. Wang, Ning & Jin, Bo & Lim, Andrew, 2015. "Target-guided algorithms for the container pre-marshalling problem," Omega, Elsevier, vol. 53(C), pages 67-77.
    14. de Melo da Silva, Marcos & Toulouse, Sophie & Wolfler Calvo, Roberto, 2018. "A new effective unified model for solving the Pre-marshalling and Block Relocation Problems," European Journal of Operational Research, Elsevier, vol. 271(1), pages 40-56.
    15. 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.
    16. Zehendner, Elisabeth & Caserta, Marco & Feillet, Dominique & Schwarze, Silvia & Voß, Stefan, 2015. "An improved mathematical formulation for the blocks relocation problem," European Journal of Operational Research, Elsevier, vol. 245(2), pages 415-422.
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    2. Jiménez-Piqueras, Celia & Ruiz, Rubén & Parreño-Torres, Consuelo & Alvarez-Valdes, Ramon, 2023. "A constraint programming approach for the premarshalling problem," European Journal of Operational Research, Elsevier, vol. 306(2), pages 668-678.
    3. Feng, Yuanjun & Song, Dong-Ping & Li, Dong, 2022. "Smart stacking for import containers using customer information at automated container terminals," European Journal of Operational Research, Elsevier, vol. 301(2), pages 502-522.
    4. Thai Doan Chuong & Xinghuo Yu & Chen Liu & Andrew Eberhard & Chaojie Li, 2024. "Solving Two-stage Quadratic Multiobjective Problems via Optimality and Relaxations," Journal of Optimization Theory and Applications, Springer, vol. 203(1), pages 676-713, October.
    5. Ignacio Araya & Martín Toledo, 2023. "A fill-and-reduce greedy algorithm for the container pre-marshalling problem," Operational Research, Springer, vol. 23(3), pages 1-29, September.
    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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