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Generating optimal and near-optimal solutions to facility location problems

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  • Richard L Church
  • Carlos A Baez

Abstract

There is a decided bent toward finding an optimal solution to a given facility location problem instance, even when there may be multiple optima or competitive near-optimal solutions. Identifying alternate solutions is often ignored in model application, even when such solutions may be preferred if they were known to exist. In this paper we discuss why generating close-to-optimal alternatives should be the preferred approach in solving spatial optimization problems, especially when it involves an application. There exists a classic approach for finding all alternate optima. This approach can be easily expanded to identify all near-optimal solutions to any discrete location model. We demonstrate the use of this technique for two classic problems: the p -median problem and the maximal covering location problem. Unfortunately, we have found that it can be mired in computational issues, even when problems are relatively small. We propose a new approach that overcomes some of these computational issues in finding alternate optima and near-optimal solutions.

Suggested Citation

  • Richard L Church & Carlos A Baez, 2020. "Generating optimal and near-optimal solutions to facility location problems," Environment and Planning B, , vol. 47(6), pages 1014-1030, July.
    • Handle: RePEc:sae:envirb:v:47:y:2020:i:6:p:1014-1030
    DOI: 10.1177/2399808320930241
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    References listed on IDEAS

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    1. DeCarolis, Joseph F., 2011. "Using modeling to generate alternatives (MGA) to expand our thinking on energy futures," Energy Economics, Elsevier, vol. 33(2), pages 145-152, March.
    2. Maria Scaparra & Richard Church & F. Medrano, 2014. "Corridor location: the multi-gateway shortest path model," Journal of Geographical Systems, Springer, vol. 16(3), pages 287-309, July.
    3. Price, James & Keppo, Ilkka, 2017. "Modelling to generate alternatives: A technique to explore uncertainty in energy-environment-economy models," Applied Energy, Elsevier, vol. 195(C), pages 356-369.
    4. E. Downey Brill, Jr., 1979. "The Use of Optimization Models in Public-Sector Planning," Management Science, INFORMS, vol. 25(5), pages 413-422, May.
    5. Andrew C. Trapp & Renata A. Konrad, 2015. "Finding diverse optima and near-optima to binary integer programs," IISE Transactions, Taylor & Francis Journals, vol. 47(11), pages 1300-1312, November.
    6. Richard L. Church & Alan Murray, 2018. "Location Covering Models," Advances in Spatial Science, Springer, number 978-3-319-99846-6, Fall.
    7. Richard Church & Charles R. Velle, 1974. "The Maximal Covering Location Problem," Papers in Regional Science, Wiley Blackwell, vol. 32(1), pages 101-118, January.
    8. Baum, Sanford & Carlson, Robert, 1979. "On solutions that are better than most," Omega, Elsevier, vol. 7(3), pages 249-255.
    9. Mark S. Daskin, 2008. "What you should know about location modeling," Naval Research Logistics (NRL), John Wiley & Sons, vol. 55(4), pages 283-294, June.
    10. S. L. Hakimi, 1965. "Optimum Distribution of Switching Centers in a Communication Network and Some Related Graph Theoretic Problems," Operations Research, INFORMS, vol. 13(3), pages 462-475, June.
    11. E. Downey Brill, Jr. & Shoou-Yuh Chang & Lewis D. Hopkins, 1982. "Modeling to Generate Alternatives: The HSJ Approach and an Illustration Using a Problem in Land Use Planning," Management Science, INFORMS, vol. 28(3), pages 221-235, March.
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