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Using tropical optimization to solve constrained minimax single-facility location problems with rectilinear distance

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  • Nikolai Krivulin

    (St. Petersburg State University)

Abstract

The aim of this paper is twofold: first, to extend the area of applications of tropical optimization by solving new constrained location problems, and second, to offer new closed-form solutions to general problems that are of interest to location analysis. We consider a constrained minimax single-facility location problem with addends on the plane with rectilinear distance. The solution commences with the representation of the problem in a standard form, and then in terms of tropical mathematics, as a constrained optimization problem. We use a transformation technique, which can act as a template to handle optimization problems in other application areas, and hence is of independent interest. To solve the constrained optimization problem, we apply methods and results of tropical optimization, which provide direct, explicit solutions. The results obtained serve to derive new solutions of the location problem, and of its special cases with reduced sets of constraints, in a closed form, ready for practical implementation and immediate computation. As illustrations, numerical solutions of example problems and their graphical representation are given. We conclude with an application of the results to optimal location of the central monitoring facility in an indoor video surveillance system in a multi-floor building environment.

Suggested Citation

  • Nikolai Krivulin, 2017. "Using tropical optimization to solve constrained minimax single-facility location problems with rectilinear distance," Computational Management Science, Springer, vol. 14(4), pages 493-518, October.
    • Handle: RePEc:spr:comgts:v:14:y:2017:i:4:d:10.1007_s10287-017-0289-2
    DOI: 10.1007/s10287-017-0289-2
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    References listed on IDEAS

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    1. ReVelle, C. S. & Eiselt, H. A., 2005. "Location analysis: A synthesis and survey," European Journal of Operational Research, Elsevier, vol. 165(1), pages 1-19, August.
    2. Hansen, Pierre & Thisse, Jacques-Francois, 1981. "Outcomes of voting and planning : Condorcet, Weber and Rawls locations," Journal of Public Economics, Elsevier, vol. 16(1), pages 1-15, August.
    3. P. M. Dearing & R. L. Francis, 1974. "A Network Flow Solution to a Multifacility Minimax Location Problem Involving Rectilinear Distances," Transportation Science, INFORMS, vol. 8(2), pages 126-141, May.
    4. Margaret L. Brandeau & Samuel S. Chiu, 1989. "An Overview of Representative Problems in Location Research," Management Science, INFORMS, vol. 35(6), pages 645-674, June.
    5. Jack Elzinga & Donald W. Hearn, 1972. "Geometrical Solutions for Some Minimax Location Problems," Transportation Science, INFORMS, vol. 6(4), pages 379-394, November.
    6. Jack Elzinga & Donald W. Hearn, 1973. "Letter to the Editor---A Note on a Minimax Location Problem," Transportation Science, INFORMS, vol. 7(1), pages 100-103, February.
    7. George O. Wesolowsky, 1972. "Rectangular Distance Location under the Minimax Optimality Criterion," Transportation Science, INFORMS, vol. 6(2), pages 103-113, May.
    8. Francis, Richard L. & McGinnis, Leon F. & White, John A., 1983. "Locational analysis," European Journal of Operational Research, Elsevier, vol. 12(3), pages 220-252, March.
    9. P. M. Dearing & R. L. Francis, 1974. "A Minimax Location Problem on a Network," Transportation Science, INFORMS, vol. 8(4), pages 333-343, November.
    10. Nikolai Krivulin, 2017. "Direct solution to constrained tropical optimization problems with application to project scheduling," Computational Management Science, Springer, vol. 14(1), pages 91-113, January.
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    Cited by:

    1. Nikolai Krivulin, 2021. "Algebraic Solution of Tropical Polynomial Optimization Problems," Mathematics, MDPI, vol. 9(19), pages 1-18, October.

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