IDEAS home Printed from https://ideas.repec.org/a/eee/proeco/v131y2011i1p392-398.html
   My bibliography  Save this article

A practical approach to sensitivity analysis in linear programming under degeneracy for management decision making

Author

Listed:
  • Koltai, Tamás
  • Tatay, Viola

Abstract

Linear programming (LP) is a widely used tool in management decision making. Theoretically, sensitivity analysis of LP problems provides useful information for the decision maker. In practice, however, most LP software provides misleading sensitivity information if the optimal solution is degenerate. The paper shows how sensitivity analysis of LP problems can be done correctly when the optimal solution is degenerate. A production planning example is presented to illustrate the incorrect sensitivity analysis results automatically provided by most LP solvers. The general characteristics of the misleading results and the possible effects of this incorrect information on management decisions are also discussed.

Suggested Citation

  • Koltai, Tamás & Tatay, Viola, 2011. "A practical approach to sensitivity analysis in linear programming under degeneracy for management decision making," International Journal of Production Economics, Elsevier, vol. 131(1), pages 392-398, May.
    • Handle: RePEc:eee:proeco:v:131:y:2011:i:1:p:392-398
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0925-5273(10)00170-2
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. David S. Rubin & Harvey M. Wagner, 1990. "Shadow Prices: Tips and Traps for Managers and Instructors," Interfaces, INFORMS, vol. 20(4), pages 150-157, August.
    2. Hadigheh, Alireza Ghaffari & Terlaky, Tamas, 2006. "Sensitivity analysis in linear optimization: Invariant support set intervals," European Journal of Operational Research, Elsevier, vol. 169(3), pages 1158-1175, March.
    3. 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.
    4. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Silvia Araújo dos Reis & José Eugenio Leal & Antônio Márcio Tavares Thomé, 2023. "A Two-Stage Stochastic Linear Programming Model for Tactical Planning in the Soybean Supply Chain," Logistics, MDPI, vol. 7(3), pages 1-26, August.
    2. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Ma, Kang-Ting & Lin, Chi-Jen & Wen, Ue-Pyng, 2013. "Type II sensitivity analysis of cost coefficients in the degenerate transportation problem," European Journal of Operational Research, Elsevier, vol. 227(2), pages 293-300.
    2. A. Ghaffari Hadigheh & K. Mirnia & T. Terlaky, 2007. "Active Constraint Set Invariancy Sensitivity Analysis in Linear Optimization," Journal of Optimization Theory and Applications, Springer, vol. 133(3), pages 303-315, June.
    3. Illes, Tibor & Terlaky, Tamas, 2002. "Pivot versus interior point methods: Pros and cons," European Journal of Operational Research, Elsevier, vol. 140(2), pages 170-190, July.
    4. Borgonovo, E., 2010. "Sensitivity analysis with finite changes: An application to modified EOQ models," European Journal of Operational Research, Elsevier, vol. 200(1), pages 127-138, January.
    5. Hadigheh, Alireza Ghaffari & Terlaky, Tamas, 2006. "Sensitivity analysis in linear optimization: Invariant support set intervals," European Journal of Operational Research, Elsevier, vol. 169(3), pages 1158-1175, March.
    6. Borgonovo, E. & Peccati, L., 2011. "Finite change comparative statics for risk-coherent inventories," International Journal of Production Economics, Elsevier, vol. 131(1), pages 52-62, May.
    7. Lin, Chi-Jen & Wen, Ue-Pyng, 2003. "Sensitivity analysis of the optimal assignment," European Journal of Operational Research, Elsevier, vol. 149(1), pages 35-46, August.
    8. M. A. Goberna & T. Terlaky & M. I. Todorov, 2010. "Sensitivity Analysis in Linear Semi-Infinite Programming via Partitions," Mathematics of Operations Research, INFORMS, vol. 35(1), pages 14-26, February.
    9. Michael, Elad & Wood, Tony A. & Manzie, Chris & Shames, Iman, 2022. "Sensitivity analysis for bottleneck assignment problems," European Journal of Operational Research, Elsevier, vol. 303(1), pages 159-167.
    10. Hladík, Milan, 2010. "Multiparametric linear programming: Support set and optimal partition invariancy," European Journal of Operational Research, Elsevier, vol. 202(1), pages 25-31, April.
    11. 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.
    12. Goberna, M.A. & Gomez, S. & Guerra, F. & Todorov, M.I., 2007. "Sensitivity analysis in linear semi-infinite programming: Perturbing cost and right-hand-side coefficients," European Journal of Operational Research, Elsevier, vol. 181(3), pages 1069-1085, September.
    13. Kavitha K. & Pandian ponnaiah, 2012. "Type II Sensitivity Analysis in Solid Assignment Problems," Modern Applied Science, Canadian Center of Science and Education, vol. 6(12), pages 1-22, December.
    14. Ehsan Salari & H. Edwin Romeijn, 2012. "Quantifying the Trade-off Between IMRT Treatment Plan Quality and Delivery Efficiency Using Direct Aperture Optimization," INFORMS Journal on Computing, INFORMS, vol. 24(4), pages 518-533, November.
    15. Borgonovo, E. & Peccati, L., 2004. "Sensitivity analysis in investment project evaluation," International Journal of Production Economics, Elsevier, vol. 90(1), pages 17-25, July.
    16. Almoustafa, Samira & Hanafi, Said & Mladenović, Nenad, 2013. "New exact method for large asymmetric distance-constrained vehicle routing problem," European Journal of Operational Research, Elsevier, vol. 226(3), pages 386-394.
    17. Terlaky, Tamas, 2001. "An easy way to teach interior-point methods," European Journal of Operational Research, Elsevier, vol. 130(1), pages 1-19, April.
    18. E. A. Yıldırım, 2003. "An Interior-Point Perspective on Sensitivity Analysis in Semidefinite Programming," Mathematics of Operations Research, INFORMS, vol. 28(4), pages 649-676, November.
    19. Koltai, Tamás, 2009. "Robustness of a production schedule to inventory cost calculations," International Journal of Production Economics, Elsevier, vol. 121(2), pages 494-504, October.
    20. Ya Ping Fang & Nan Jing Huang & Xiao Qi Yang, 2012. "Local Smooth Representations of Parametric Semiclosed Polyhedra with Applications to Sensitivity in Piecewise Linear Programs," Journal of Optimization Theory and Applications, Springer, vol. 155(3), pages 810-839, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:proeco:v:131:y:2011:i:1:p:392-398. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/ijpe .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.