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Standard sensitivity analysis and additive tolerance approach in MOLP

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  • Sebastian Sitarz

Abstract

We consider sensitivity analysis of the objective function coefficients in multiple objective linear programming (MOLP). We focus on the properties of the parameters set for which a given extreme solution is efficient. Moreover, we compare two approaches: the standard sensitivity analysis (changing only one coefficient) and the additive tolerance approach (changing all coefficients). We find the connections between these two approaches by giving a theorem describing the upper bound on the maximal additive tolerance. Copyright Springer Science+Business Media, LLC 2010

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  • Sebastian Sitarz, 2010. "Standard sensitivity analysis and additive tolerance approach in MOLP," Annals of Operations Research, Springer, vol. 181(1), pages 219-232, December.
    • Handle: RePEc:spr:annopr:v:181:y:2010:i:1:p:219-232:10.1007/s10479-010-0728-8
    DOI: 10.1007/s10479-010-0728-8
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    References listed on IDEAS

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    1. Sitarz, Sebastian, 2008. "Postoptimal analysis in multicriteria linear programming," European Journal of Operational Research, Elsevier, vol. 191(1), pages 7-18, November.
    2. Benson, Harold P. & Sun, Erjiang, 2002. "A weight set decomposition algorithm for finding all efficient extreme points in the outcome set of a multiple objective linear program," European Journal of Operational Research, Elsevier, vol. 139(1), pages 26-41, May.
    3. Pereira Borges, Ana Rosa & Henggeler Antunes, Carlos, 2002. "A visual interactive tolerance approach to sensitivity analysis in MOLP," European Journal of Operational Research, Elsevier, vol. 142(2), pages 357-381, October.
    4. Oliveira, Carla & Antunes, Carlos Henggeler, 2007. "Multiple objective linear programming models with interval coefficients - an illustrated overview," European Journal of Operational Research, Elsevier, vol. 181(3), pages 1434-1463, September.
    5. Hansen, Pierre & Labbe, Martine & Wendell, Richard E., 1989. "Sensitivity analysis in multiple objective linear programming: The tolerance approach," European Journal of Operational Research, Elsevier, vol. 38(1), pages 63-69, January.
    6. Gal, Tomas & Wolf, Karin, 1986. "Stability in vector maximization--A survey," European Journal of Operational Research, Elsevier, vol. 25(2), pages 169-182, May.
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    Cited by:

    1. Georgiev, Pando Gr. & Luc, Dinh The & Pardalos, Panos M., 2013. "Robust aspects of solutions in deterministic multiple objective linear programming," European Journal of Operational Research, Elsevier, vol. 229(1), pages 29-36.
    2. Sebastian Sitarz, 2013. "Compromise programming with Tchebycheff norm for discrete stochastic orders," Annals of Operations Research, Springer, vol. 211(1), pages 433-446, December.
    3. Hladík, Milan & Sitarz, Sebastian, 2013. "Maximal and supremal tolerances in multiobjective linear programming," European Journal of Operational Research, Elsevier, vol. 228(1), pages 93-101.

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