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Minimising the maximum relative regret for linear programmes with interval objective function coefficients

Author

Listed:
  • H E Mausser

    (Algorithmics Incorporated)

  • M Laguna

    (University of Colorado)

Abstract

The minimax relative regret solution to a linear programme with interval objective function coefficients can be found using an algorithm that, at each iteration, solves a linear programme to generate a candidate solution and a mixed integer programme (MIP) to find the corresponding maximum regret. This paper first shows that there exists a regret-maximising solution in which all uncertain costs are at a bound, and then uses this to derive a MIP formulation that maximises the regret of a candidate solution. Computational experiments demonstrate that this approach is effective for problems with up to 50 uncertain objective function coefficients, significantly improving upon the existing enumerative method.

Suggested Citation

  • H E Mausser & M Laguna, 1999. "Minimising the maximum relative regret for linear programmes with interval objective function coefficients," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 50(10), pages 1063-1070, October.
    • Handle: RePEc:pal:jorsoc:v:50:y:1999:i:10:d:10.1057_palgrave.jors.2600789
    DOI: 10.1057/palgrave.jors.2600789
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    Citations

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    Cited by:

    1. A O Kazakçi & S Rozakis & D Vanderpooten, 2007. "Energy crop supply in France: a min-max regret approach," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 58(11), pages 1470-1479, November.
    2. Zhizhu Lai & Qun Yue & Zheng Wang & Dongmei Ge & Yulong Chen & Zhihong Zhou, 2022. "The min-p robust optimization approach for facility location problem under uncertainty," Journal of Combinatorial Optimization, Springer, vol. 44(2), pages 1134-1160, September.
    3. Thomas A. Weber, 2023. "Relatively robust decisions," Theory and Decision, Springer, vol. 94(1), pages 35-62, January.
    4. Rozakis, Stelios, 2011. "Impacts of flatter rates and environmental top-ups in Greece: A novel mathematical modeling approach," Agricultural Economics Review, Greek Association of Agricultural Economists, vol. 12(2).
    5. Jihee Han & KwangSup Shin, 2016. "Evaluation mechanism for structural robustness of supply chain considering disruption propagation," International Journal of Production Research, Taylor & Francis Journals, vol. 54(1), pages 135-151, January.
    6. Amadeu Almeida Coco & João Carlos Abreu Júnior & Thiago F. Noronha & Andréa Cynthia Santos, 2017. "Erratum to: An integer linear programming formulation and heuristics for the minmax relative regret robust shortest path problem," Journal of Global Optimization, Springer, vol. 68(2), pages 463-466, June.
    7. Masahiro Inuiguchi & Zhenzhong Gao & Carla Oliveira Henriques, 2023. "Robust optimality analysis of non-degenerate basic feasible solutions in linear programming problems with fuzzy objective coefficients," Fuzzy Optimization and Decision Making, Springer, vol. 22(1), pages 51-79, March.
    8. Dimitris Bertsimas & Iain Dunning, 2020. "Relative Robust and Adaptive Optimization," INFORMS Journal on Computing, INFORMS, vol. 32(2), pages 408-427, April.
    9. Henriques, C.O. & Inuiguchi, M. & Luque, M. & Figueira, J.R., 2020. "New conditions for testing necessarily/possibly efficiency of non-degenerate basic solutions based on the tolerance approach," European Journal of Operational Research, Elsevier, vol. 283(1), pages 341-355.
    10. Mavrotas, George & Diakoulaki, Danae & Florios, Kostas & Georgiou, Paraskevas, 2008. "A mathematical programming framework for energy planning in services' sector buildings under uncertainty in load demand: The case of a hospital in Athens," Energy Policy, Elsevier, vol. 36(7), pages 2415-2429, July.
    11. Georgios P. Trachanas & Aikaterini Forouli & Nikolaos Gkonis & Haris Doukas, 2020. "Hedging uncertainty in energy efficiency strategies: a minimax regret analysis," Operational Research, Springer, vol. 20(4), pages 2229-2244, December.
    12. Xidonas, Panos & Mavrotas, George & Hassapis, Christis & Zopounidis, Constantin, 2017. "Robust multiobjective portfolio optimization: A minimax regret approach," European Journal of Operational Research, Elsevier, vol. 262(1), pages 299-305.
    13. Xidonas, Panos & Hassapis, Christis & Soulis, John & Samitas, Aristeidis, 2017. "Robust minimum variance portfolio optimization modelling under scenario uncertainty," Economic Modelling, Elsevier, vol. 64(C), pages 60-71.

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