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Improved exact approaches for row layout problems with departments of equal length

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  • Anjos, Miguel F.
  • Fischer, Anja
  • Hungerländer, Philipp
Abstract
Facility layout is a well-known operations research problem that arises in various applications. The multi-row layout is a challenging optimization problem where the task is to determine the optimal placement of one-dimensional departments on a given number of rows. This paper is concerned with multi-row facility layout problems in which all the departments have the same length. This is an important special case that includes most multi-row facility layout applications from the literature. We prove two theoretical results about the structure of optimal layouts, namely that only spaces of unit length are necessary to obtain an optimal solution, and that exact expressions exist for the minimum number of such spaces that need to be added so as to preserve at least one global optimal solution. Using these results we propose a binary linear optimization model and a binary semidefinite optimization model for the problem, neither of which uses continuous variables, which has a significant positive computational impact. Our computational experiments show that our specially tailored approaches can handle much larger instances than other exact methods applicable to this important problem class.

Suggested Citation

  • Anjos, Miguel F. & Fischer, Anja & Hungerländer, Philipp, 2018. "Improved exact approaches for row layout problems with departments of equal length," European Journal of Operational Research, Elsevier, vol. 270(2), pages 514-529.
    • Handle: RePEc:eee:ejores:v:270:y:2018:i:2:p:514-529
    DOI: 10.1016/j.ejor.2018.04.008
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    References listed on IDEAS

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    1. Miguel F. Anjos & Jean B. Lasserre, 2012. "Introduction to Semidefinite, Conic and Polynomial Optimization," International Series in Operations Research & Management Science, in: Miguel F. Anjos & Jean B. Lasserre (ed.), Handbook on Semidefinite, Conic and Polynomial Optimization, chapter 0, pages 1-22, Springer.
    2. Loiola, Eliane Maria & de Abreu, Nair Maria Maia & Boaventura-Netto, Paulo Oswaldo & Hahn, Peter & Querido, Tania, 2007. "A survey for the quadratic assignment problem," European Journal of Operational Research, Elsevier, vol. 176(2), pages 657-690, January.
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    4. Anjos, Miguel F. & Vieira, Manuel V.C., 2017. "Mathematical optimization approaches for facility layout problems: The state-of-the-art and future research directions," European Journal of Operational Research, Elsevier, vol. 261(1), pages 1-16.
    5. Miguel F. Anjos & Frauke Liers, 2012. "Global Approaches for Facility Layout and VLSI Floorplanning," International Series in Operations Research & Management Science, in: Miguel F. Anjos & Jean B. Lasserre (ed.), Handbook on Semidefinite, Conic and Polynomial Optimization, chapter 0, pages 849-877, Springer.
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    11. Kothari, Ravi & Ghosh, Diptesh, 2012. "Sensitivity Analysis for the Single Row Facility Layout Problem," IIMA Working Papers WP2012-04-02, Indian Institute of Management Ahmedabad, Research and Publication Department.
    12. Hungerländer, Philipp & Anjos, Miguel F., 2015. "A semidefinite optimization-based approach for global optimization of multi-row facility layout," European Journal of Operational Research, Elsevier, vol. 245(1), pages 46-61.
    13. Kothari, Ravi & Ghosh, Diptesh, 2012. "Scatter Search Algorithms for the Single Row Facility Layout Problem," IIMA Working Papers WP2012-04-01, Indian Institute of Management Ahmedabad, Research and Publication Department.
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    Cited by:

    1. Weckenborg, Christian & Schumacher, Patrick & Thies, Christian & Spengler, Thomas S., 2024. "Flexibility in manufacturing system design: A review of recent approaches from Operations Research," European Journal of Operational Research, Elsevier, vol. 315(2), pages 413-441.
    2. Gintaras Palubeckis, 2020. "An Approach Integrating Simulated Annealing and Variable Neighborhood Search for the Bidirectional Loop Layout Problem," Mathematics, MDPI, vol. 9(1), pages 1-30, December.
    3. Dahlbeck, Mirko & Fischer, Anja & Fischer, Frank, 2020. "Decorous combinatorial lower bounds for row layout problems," European Journal of Operational Research, Elsevier, vol. 286(3), pages 929-944.
    4. Dahlbeck, Mirko & Fischer, Anja & Fischer, Frank & Hungerländer, Philipp & Maier, Kerstin, 2023. "Exact approaches for the combined cell layout problem," European Journal of Operational Research, Elsevier, vol. 305(2), pages 530-546.
    5. Wu, Song & Yang, Wei & Hanafi, Saïd & Wilbaut, Christophe & Wang, Yang, 2024. "Iterated local search with ejection chains for the space-free multi-row facility layout problem," European Journal of Operational Research, Elsevier, vol. 316(3), pages 873-886.
    6. Dahlbeck, Mirko, 2021. "A mixed-integer linear programming approach for the T-row and the multi-bay facility layout problem," European Journal of Operational Research, Elsevier, vol. 295(2), pages 443-462.

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