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A unifying framework for duality and modeling in robust linear programs

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  • Soyster, A.L.
  • Murphy, F.H.

Abstract

In this paper, our major theme is a unifying framework for duality in robust linear programming. We show that there are two pair of dual programs allied with a robust linear program; one in which the primal is constructed to be “ultra-conservative” and one in which the primal is constructed to be “ultra-optimistic.” Furthermore, as one would expect, if the uncertainly in the primal is row-based, the corresponding uncertainty in the dual is column-based, and vice-versa. Several examples are provided that illustrate the properties of these primal and dual models.

Suggested Citation

  • Soyster, A.L. & Murphy, F.H., 2013. "A unifying framework for duality and modeling in robust linear programs," Omega, Elsevier, vol. 41(6), pages 984-997.
    • Handle: RePEc:eee:jomega:v:41:y:2013:i:6:p:984-997
    DOI: 10.1016/j.omega.2012.10.006
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    References listed on IDEAS

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    1. Dimitris Bertsimas & Melvyn Sim, 2004. "The Price of Robustness," Operations Research, INFORMS, vol. 52(1), pages 35-53, February.
    2. J W Chinneck & K Ramadan, 2000. "Linear programming with interval coefficients," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 51(2), pages 209-220, February.
    3. Soyster, A. L., 1979. "Inexact linear programming with generalized resource sets," European Journal of Operational Research, Elsevier, vol. 3(4), pages 316-321, July.
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    5. A. Ben-Tal & A. Nemirovski, 1998. "Robust Convex Optimization," Mathematics of Operations Research, INFORMS, vol. 23(4), pages 769-805, November.
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    Cited by:

    1. Mavrotas, George & Figueira, José Rui & Siskos, Eleftherios, 2015. "Robustness analysis methodology for multi-objective combinatorial optimization problems and application to project selection," Omega, Elsevier, vol. 52(C), pages 142-155.
    2. Hladík, Milan, 2016. "Robust optimal solutions in interval linear programming with forall-exists quantifiers," European Journal of Operational Research, Elsevier, vol. 254(3), pages 705-714.
    3. Ali Haddad-Sisakht & Sarah M. Ryan, 2018. "Conditions under which adjustability lowers the cost of a robust linear program," Annals of Operations Research, Springer, vol. 269(1), pages 185-204, October.
    4. Bruni, M.E. & Di Puglia Pugliese, L. & Beraldi, P. & Guerriero, F., 2017. "An adjustable robust optimization model for the resource-constrained project scheduling problem with uncertain activity durations," Omega, Elsevier, vol. 71(C), pages 66-84.
    5. Nalan Gülpınar & Dessislava Pachamanova & Ethem Çanakoğlu, 2016. "A robust asset–liability management framework for investment products with guarantees," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 38(4), pages 1007-1041, October.
    6. Soyster, A.L. & Murphy, F.H., 2017. "Data driven matrix uncertainty for robust linear programming," Omega, Elsevier, vol. 70(C), pages 43-57.
    7. Andreas Thorsen & Tao Yao, 2017. "Robust inventory control under demand and lead time uncertainty," Annals of Operations Research, Springer, vol. 257(1), pages 207-236, October.
    8. Valle, C.A. & Meade, N. & Beasley, J.E., 2014. "Absolute return portfolios," Omega, Elsevier, vol. 45(C), pages 20-41.
    9. Gülpınar, Nalân & Çanakoḡlu, Ethem, 2017. "Robust portfolio selection problem under temperature uncertainty," European Journal of Operational Research, Elsevier, vol. 256(2), pages 500-523.
    10. Gorissen, Bram L. & Yanıkoğlu, İhsan & den Hertog, Dick, 2015. "A practical guide to robust optimization," Omega, Elsevier, vol. 53(C), pages 124-137.

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    Keywords

    Robust linear programming; Duality;

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