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On the unboundedness of facility layout problems

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  • Zvi Drezner

Abstract

Facility layout problems involve the location of facilities in a planar arrangement such that facilities that are strongly connected to one another are close to each other and facilities that are not connected may be far from one another. Pairs of facilities that have a negative connection should be far from one another. Most solution procedures assume that the optimal arrangement is bounded and thus do not incorporate constraints on the location of facilities. However, especially when some of the coefficients are negative, it is possible that the optimal configuration is unbounded. In this paper we investigate whether the solution to the facility layout problem is bounded or not. The main Theorem is a necessary and sufficient condition for boundedness. Sufficient conditions that prove boundedness or unboundedness are also given. Copyright Springer-Verlag 2010

Suggested Citation

  • Zvi Drezner, 2010. "On the unboundedness of facility layout problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 72(2), pages 205-216, October.
    • Handle: RePEc:spr:mathme:v:72:y:2010:i:2:p:205-216
    DOI: 10.1007/s00186-010-0317-2
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    References listed on IDEAS

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    1. Zvi Drezner, 1987. "A Heuristic Procedure for the Layout of a Large Number of Facilities," Management Science, INFORMS, vol. 33(7), pages 907-915, July.
    2. 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.
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    4. Zvi Drezner & Peter Hahn & Éeric Taillard, 2005. "Recent Advances for the Quadratic Assignment Problem with Special Emphasis on Instances that are Difficult for Meta-Heuristic Methods," Annals of Operations Research, Springer, vol. 139(1), pages 65-94, October.
    5. Miguel F. Anjos & Anthony Vannelli, 2006. "A New Mathematical-Programming Framework for Facility-Layout Design," INFORMS Journal on Computing, INFORMS, vol. 18(1), pages 111-118, February.
    6. Castillo, Ignacio & Kampas, Frank J. & Pintér, János D., 2008. "Solving circle packing problems by global optimization: Numerical results and industrial applications," European Journal of Operational Research, Elsevier, vol. 191(3), pages 786-802, December.
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    Cited by:

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