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Min-Max Regret Robust Optimization Approach on Interval Data Uncertainty

Author

Listed:
  • T. Assavapokee

    (University of Houston)

  • M. J. Realff

    (Georgia Institute of Technology)

  • J. C. Ammons

    (Georgia Institute of Technology)

Abstract

This paper presents a three-stage optimization algorithm for solving two-stage deviation robust decision making problems under uncertainty. The structure of the first-stage problem is a mixed integer linear program and the structure of the second-stage problem is a linear program. Each uncertain model parameter can independently take its value from a real compact interval with unknown probability distribution. The algorithm coordinates three mathematical programming formulations to iteratively solve the overall problem. This paper provides the application of the algorithm on the robust facility location problem and a counterexample illustrating the insufficiency of the solution obtained by considering only a finite number of scenarios generated by the endpoints of all intervals.

Suggested Citation

  • T. Assavapokee & M. J. Realff & J. C. Ammons, 2008. "Min-Max Regret Robust Optimization Approach on Interval Data Uncertainty," Journal of Optimization Theory and Applications, Springer, vol. 137(2), pages 297-316, May.
    • Handle: RePEc:spr:joptap:v:137:y:2008:i:2:d:10.1007_s10957-007-9334-6
    DOI: 10.1007/s10957-007-9334-6
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    References listed on IDEAS

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    1. A. Ben-Tal & A. Nemirovski, 1998. "Robust Convex Optimization," Mathematics of Operations Research, INFORMS, vol. 23(4), pages 769-805, November.
    2. Dimitris Bertsimas & Melvyn Sim, 2004. "The Price of Robustness," Operations Research, INFORMS, vol. 52(1), pages 35-53, February.
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    Cited by:

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    3. Jungho Park & Hadi El-Amine & Nevin Mutlu, 2021. "An Exact Algorithm for Large-Scale Continuous Nonlinear Resource Allocation Problems with Minimax Regret Objectives," INFORMS Journal on Computing, INFORMS, vol. 33(3), pages 1213-1228, July.
    4. Henao, Felipe & Dyner, Isaac, 2020. "Renewables in the optimal expansion of colombian power considering the Hidroituango crisis," Renewable Energy, Elsevier, vol. 158(C), pages 612-627.
    5. Henao, Felipe & Rodriguez, Yeny & Viteri, Juan Pablo & Dyner, Isaac, 2019. "Optimising the insertion of renewables in the Colombian power sector," Renewable Energy, Elsevier, vol. 132(C), pages 81-92.
    6. Eduardo Conde, 2014. "A Minmax Regret Linear Regression Model Under Uncertainty in the Dependent Variable," Journal of Optimization Theory and Applications, Springer, vol. 160(2), pages 573-596, February.
    7. Pejman Peykani & Jafar Gheidar-Kheljani & Reza Farzipoor Saen & Emran Mohammadi, 2022. "Generalized robust window data envelopment analysis approach for dynamic performance measurement under uncertain panel data," Operational Research, Springer, vol. 22(5), pages 5529-5567, November.
    8. Yokoyama, Ryohei & Tokunaga, Akira & Wakui, Tetsuya, 2018. "Robust optimal design of energy supply systems under uncertain energy demands based on a mixed-integer linear model," Energy, Elsevier, vol. 153(C), pages 159-169.
    9. Dimitris Bertsimas & Iain Dunning, 2020. "Relative Robust and Adaptive Optimization," INFORMS Journal on Computing, INFORMS, vol. 32(2), pages 408-427, April.
    10. Yokoyama, Ryohei & Nakamura, Ryo & Wakui, Tetsuya, 2017. "Performance comparison of energy supply systems under uncertain energy demands based on a mixed-integer linear model," Energy, Elsevier, vol. 137(C), pages 878-887.
    11. Pejman Peykani & Roya Soltani & Cristina Tanasescu & Seyed Ehsan Shojaie & Alireza Jandaghian, 2025. "The Robust Malmquist Productivity Index: A Framework for Measuring Productivity Changes over Time Under Uncertainty," Mathematics, MDPI, vol. 13(11), pages 1-27, May.

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