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The Tolerance Approach to Sensitivity Analysis of Matrix Coefficients in Linear Programming

Author

Listed:
  • N. Ravi

    (AT&T Bell Laboratories, Crawfords Corner Road, Room 3J-527, Holmdel, New Jersey 07733)

  • Richard E. Wendell

    (Graduate School of Business, University of Pittsburgh, Pittsburgh, Pennsylvania 15260)

Abstract

The tolerance approach to sensitivity analysis allows for simultaneous and independent variations of the elements of a column or a row of the coefficient matrix in a standard linear programming problem. In particular, the approach yields a maximum tolerance percentage within which the elements of a column may all vary simultaneously and independently from their estimated values while still retaining the same set of basic variables in an optimal solution. A similar result is also derived for the perturbations of the elements of a row.

Suggested Citation

  • N. Ravi & Richard E. Wendell, 1989. "The Tolerance Approach to Sensitivity Analysis of Matrix Coefficients in Linear Programming," Management Science, INFORMS, vol. 35(9), pages 1106-1119, September.
    • Handle: RePEc:inm:ormnsc:v:35:y:1989:i:9:p:1106-1119
    DOI: 10.1287/mnsc.35.9.1106
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    Citations

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    Cited by:

    1. Vyacheslav V. Chistyakov & Panos M. Pardalos, 2015. "Stability Analysis in Discrete Optimization Involving Generalized Addition Operations," Journal of Optimization Theory and Applications, Springer, vol. 167(2), pages 585-616, November.
    2. 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.
    3. Harvey J. Greenberg, 1999. "Matrix Sensitivity Analysis from an Interior Solution of a Linear Program," INFORMS Journal on Computing, INFORMS, vol. 11(3), pages 316-327, August.
    4. C. Oliveira & D. Coelho & C. H. Antunes, 2016. "Coupling input–output analysis with multiobjective linear programming models for the study of economy–energy–environment–social (E3S) trade-offs: a review," Annals of Operations Research, Springer, vol. 247(2), pages 471-502, December.
    5. Singh, Sanjeet & Gupta, Pankaj & Bhatia, Davinder, 2005. "Multiparametric sensitivity analysis in programming problem with linear-plus-linear fractional objective function," European Journal of Operational Research, Elsevier, vol. 160(1), pages 232-241, January.
    6. Borgonovo, Emanuele & Plischke, Elmar, 2016. "Sensitivity analysis: A review of recent advances," European Journal of Operational Research, Elsevier, vol. 248(3), pages 869-887.
    7. Marmol, A. M. & Puerto, J., 1997. "Special cases of the tolerance approach in multiobjective linear programming," European Journal of Operational Research, Elsevier, vol. 98(3), pages 610-616, May.
    8. Borgonovo, Emanuele & Buzzard, Gregery T. & Wendell, Richard E., 2018. "A global tolerance approach to sensitivity analysis in linear programming," European Journal of Operational Research, Elsevier, vol. 267(1), pages 321-337.

    More about this item

    Keywords

    linear programming; sensitivity analysis;

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