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A concept of a robust solution of a multicriterial linear programming problem

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  • Dorota Kuchta

Abstract

A new concept of a robust solution of a multicriterial linear programming problem is proposed. The robust solution is understood here as the best starting point, prepared while the preferences of the decision maker with respect to the criteria are still unknown, for the adaptation of the solution to the preferences of the decision maker, once they are finally known. The objective is the total cost of the initial preparation and of the later potential adaptation of the solution. In the starting robust solution the decision variables may have interval values. The problem can be solved by means of the simplex algorithm. A numerical example illustrates the approach. Copyright The Author(s) 2011

Suggested Citation

  • Dorota Kuchta, 2011. "A concept of a robust solution of a multicriterial linear programming problem," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 19(4), pages 605-613, December.
    • Handle: RePEc:spr:cejnor:v:19:y:2011:i:4:p:605-613
    DOI: 10.1007/s10100-010-0150-y
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    References listed on IDEAS

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    1. El-Banna, Abou-Zaid H. & Zarea, Sana’a A., 2001. "Stability of linear vector optimization problems corresponding to an efficient set," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 57(6), pages 335-345.
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    Cited by:

    1. Jerzy Grobelny & Rafał Michalski, 2020. "Effects of scatter plot initial solutions on regular grid facility layout algorithms in typical production models," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 28(2), pages 601-632, June.
    2. P. Kumar & A. K. Bhurjee, 2022. "Multi-objective enhanced interval optimization problem," Annals of Operations Research, Springer, vol. 311(2), pages 1035-1050, April.
    3. Antonio G. Martín & Manuel Díaz-Madroñero & Josefa Mula, 2020. "Master production schedule using robust optimization approaches in an automobile second-tier supplier," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 28(1), pages 143-166, March.
    4. Hanks, Robert W. & Lunday, Brian J. & Weir, Jeffery D., 2020. "Robust goal programming for multi-objective optimization of data-driven problems: A use case for the United States transportation command's liner rate setting problem," Omega, Elsevier, vol. 90(C).

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      Keywords

      Multicriteria programming; Robust solution;

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