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Equivalent instances of the simple plant location problem

Author

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  • Ghosh, Diptesh
  • Sierksma, Gerard
  • Goldengorin, Boris
  • AlMohammad, Bader F.

    (Groningen University)

Abstract

In this paper we deal with a pseudo-Boolean representation of the simple plant location problem. We define instances of this problem that are equivalent, in the sense that each feasible solution has the same goal function value in all such instances. We further define a collection of polytopes whose union describes the set of instances equivalent to a given instance. We use the concept of equivalence to develop a method by which we can extend the set of instances that we can solve using our knowledge of polynomially solvable special cases. We also present a new preprocessing rule that allows us to determine sites in which facilities will not be located in an optimal solution and thereby reduce the size of a problem instance.

Suggested Citation

  • Ghosh, Diptesh & Sierksma, Gerard & Goldengorin, Boris & AlMohammad, Bader F., 2000. "Equivalent instances of the simple plant location problem," Research Report 00A54, University of Groningen, Research Institute SOM (Systems, Organisations and Management).
    • Handle: RePEc:gro:rugsom:00a54
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    File URL: http://irs.ub.rug.nl/ppn/240966023
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    References listed on IDEAS

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    1. Charles S. Revelle & Gilbert Laporte, 1996. "The Plant Location Problem: New Models and Research Prospects," Operations Research, INFORMS, vol. 44(6), pages 864-874, December.
    2. Boris Goldengorin & Gerard Sierksma & Gert A. Tijssen & Michael Tso, 1999. "The Data-Correcting Algorithm for the Minimization of Supermodular Functions," Management Science, INFORMS, vol. 45(11), pages 1539-1551, November.
    3. P. M. Dearing & P. L. Hammer & B. Simeone, 1992. "Boolean and Graph Theoretic Formulations of the Simple Plant Location Problem," Transportation Science, INFORMS, vol. 26(2), pages 138-148, May.
    4. David W. Pentico, 1976. "The Assortment Problem with Nonlinear Cost Functions," Operations Research, INFORMS, vol. 24(6), pages 1129-1142, December.
    5. David W. Pentico, 1988. "The Discrete Two-Dimensional Assortment Problem," Operations Research, INFORMS, vol. 36(2), pages 324-332, April.
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    2. Goldengorin, Boris & Ghosh, Diptesh & Sierksma, Gerard, 2001. "Branch and peg algorithms for the simple plant location problem," Research Report 01A14, University of Groningen, Research Institute SOM (Systems, Organisations and Management).
    3. Vincent Tulasi & Isaac Kwasi Adu & Elikem Kofi Krampa, 2016. "Location of Farmers Warehouse at Adaklu Traditional Area, Volta Region, Ghana," Journal of Optimization, Hindawi, vol. 2016, pages 1-10, July.
    4. repec:dgr:rugsom:01a53 is not listed on IDEAS
    5. Goldengorin, Boris, 2001. "Solving the simple plant location problem using a data correcting approach," Research Report 01A53, University of Groningen, Research Institute SOM (Systems, Organisations and Management).

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