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Sensitivity analysis of linear programming in the presence of correlation among right-hand side parameters or objective function coefficients

Author

Listed:
  • Amir Shahin

    () (Islamic Azad University)

  • Payam Hanafizadeh

    () (Allameh Tabataba’i University)

  • Milan Hladík

    () (Charles University in Prague)

Abstract

Abstract In the literature, sensitivity analysis of linear programming (LP) has been widely studied. However, only some very simple and special cases were considered when right-hand side (RHS) parameters or objective function coefficients (OFC) correlate to each other. In the presence of correlation when one parameter changes, other parameters vary, too. Here principal component analysis is used to convert the correlation of the LP homogenous parameters into functional relations. Then, using the derivatives of the functional relations, it is possible to perform classical sensitivity analysis for the LP with correlation among RHS parameters or OFC. The validity of the devised method is corroborated by open literature examples having correlation among homogenous parameters.

Suggested Citation

  • Amir Shahin & Payam Hanafizadeh & Milan Hladík, 2016. "Sensitivity analysis of linear programming in the presence of correlation among right-hand side parameters or objective function coefficients," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 24(3), pages 563-593, September.
  • Handle: RePEc:spr:cejnor:v:24:y:2016:i:3:d:10.1007_s10100-014-0353-8
    DOI: 10.1007/s10100-014-0353-8
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    References listed on IDEAS

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    1. Richard E. Wendell, 1985. "The Tolerance Approach to Sensitivity Analysis in Linear Programming," Management Science, INFORMS, vol. 31(5), pages 564-578, May.
    2. Jansen, B. & de Jong, J. J. & Roos, C. & Terlaky, T., 1997. "Sensitivity analysis in linear programming: just be careful!," European Journal of Operational Research, Elsevier, vol. 101(1), pages 15-28, August.
    3. Koltai, Tamas & Terlaky, Tamas, 2000. "The difference between the managerial and mathematical interpretation of sensitivity analysis results in linear programming," International Journal of Production Economics, Elsevier, vol. 65(3), pages 257-274, May.
    4. 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.
    5. Sebastian Sitarz, 2010. "Standard sensitivity analysis and additive tolerance approach in MOLP," Annals of Operations Research, Springer, vol. 181(1), pages 219-232, December.
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    1. repec:eee:ejores:v:267:y:2018:i:1:p:321-337 is not listed on IDEAS

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