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A convex optimisation framework for the unequal-areas facility layout problem


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  • Jankovits, Ibolya
  • Luo, Chaomin
  • Anjos, Miguel F.
  • Vannelli, Anthony
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    The unequal-areas facility layout problem is concerned with finding the optimal arrangement of a given number of non-overlapping indivisible departments with unequal area requirements within a facility. We present a convex-optimisation-based framework for efficiently finding competitive solutions for this problem. The framework is based on the combination of two mathematical programming models. The first model is a convex relaxation of the layout problem that establishes the relative position of the departments within the facility, and the second model uses semidefinite optimisation to determine the final layout. Aspect ratio constraints, frequently used in facility layout methods to restrict the occurrence of overly long and narrow departments in the computed layouts, are taken into account by both models. We present computational results showing that the proposed framework consistently produces competitive, and often improved, layouts for well-known large instances when compared with other approaches in the literature.

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    Bibliographic Info

    Article provided by Elsevier in its journal European Journal of Operational Research.

    Volume (Year): 214 (2011)
    Issue (Month): 2 (October)
    Pages: 199-215

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    Handle: RePEc:eee:ejores:v:214:y:2011:i:2:p:199-215

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    Keywords: Facility layout Semidefinite programming Convex programming Global optimisation;


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    1. Gordon C. Armour & Elwood S. Buffa, 1963. "A Heuristic Algorithm and Simulation Approach to Relative Location of Facilities," Management Science, INFORMS, vol. 9(2), pages 294-309, January.
    2. Kar Yan Tam, 1992. "Genetic algorithms, function optimization, and facility layout design," European Journal of Operational Research, Elsevier, vol. 63(2), pages 322-346, December.
    3. Bock, Stefan & Hoberg, Kai, 2007. "Detailed layout planning for irregularly-shaped machines with transportation path design," European Journal of Operational Research, Elsevier, vol. 177(2), pages 693-718, March.
    4. Michael Scriabin & Roger C. Vergin, 1975. "Comparison of Computer Algorithms and Visual Based Methods for Plant Layout," Management Science, INFORMS, vol. 22(2), pages 172-181, October.
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