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Sensitivity Analysis and Uncertainty in Linear Programming

Author

Listed:
  • Julia L. Higle

    (Department of Systems and Industrial Engineering, University of Arizona, Tucson, Arizona 85721)

  • Stein W. Wallace

    (Molde University College, PO Box 2110, N-6402 Molde, Norway)

Abstract

Linear programming (LP) is one of the great successes to emerge from operations research and management science. It is well developed and widely used. LP problems in practice are often based on numerical data that represent rough approximations of quantities that are inherently difficult to estimate. Because of this, most LP-based studies include a postoptimality investigation of how a change in the data changes the solution. Researchers routinely undertake this type of sensitivity analysis (SA), and most commercial packages for solving linear programs include the results of such an analysis as part of the standard output report. SA has shortcomings that run contrary to conventional wisdom. Alternate models address these shortcomings.

Suggested Citation

  • Julia L. Higle & Stein W. Wallace, 2003. "Sensitivity Analysis and Uncertainty in Linear Programming," Interfaces, INFORMS, vol. 33(4), pages 53-60, August.
    • Handle: RePEc:inm:orinte:v:33:y:2003:i:4:p:53-60
    DOI: 10.1287/inte.33.4.53.16370
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    Citations

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    Cited by:

    1. 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.
    2. Xin Wang & Stein W. Wallace, 2016. "Stochastic scheduled service network design in the presence of a spot market for excess capacity," EURO Journal on Transportation and Logistics, Springer;EURO - The Association of European Operational Research Societies, vol. 5(4), pages 393-413, December.
    3. Fatemeh Sarayloo & Teodor Gabriel Crainic & Walter Rei, 2021. "A Learning-Based Matheuristic for Stochastic Multicommodity Network Design," INFORMS Journal on Computing, INFORMS, vol. 33(2), pages 643-656, May.
    4. Hui, Yer Van & Gao, Jia & Leung, Lawrence & Wallace, Stein, 2014. "Airfreight forwarder’s shipment planning under uncertainty: A two-stage stochastic programming approach," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 66(C), pages 83-102.
    5. 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.
    6. Z.N. Chen & C.K.M. Lee & W.H. Ip & G.T.S. Ho, 2012. "Design and evaluation of an integrated inventory and transportation system," Transportation Planning and Technology, Taylor & Francis Journals, vol. 35(4), pages 491-507, January.
    7. Francesca Maggioni & Stein Wallace, 2012. "Analyzing the quality of the expected value solution in stochastic programming," Annals of Operations Research, Springer, vol. 200(1), pages 37-54, November.
    8. Arnt-Gunnar Lium & Teodor Gabriel Crainic & Stein W. Wallace, 2009. "A Study of Demand Stochasticity in Service Network Design," Transportation Science, INFORMS, vol. 43(2), pages 144-157, May.
    9. Stein Wallace, 2010. "Stochastic programming and the option of doing it differently," Annals of Operations Research, Springer, vol. 177(1), pages 3-8, June.
    10. Fatemeh Sarayloo & Teodor Gabriel Crainic & Walter Rei, 2021. "A reduced cost-based restriction and refinement matheuristic for stochastic network design problem," Journal of Heuristics, Springer, vol. 27(3), pages 325-351, June.
    11. Biju Thapalia & Stein Wallace & Michal Kaut & Teodor Crainic, 2012. "Single source single-commodity stochastic network design," Computational Management Science, Springer, vol. 9(1), pages 139-160, February.
    12. E. Borgonovo & L. Peccati, 2011. "Managerial insights from service industry models: a new scenario decomposition method," Annals of Operations Research, Springer, vol. 185(1), pages 161-179, May.
    13. Thapalia, Biju K. & Crainic, Teodor Gabriel & Kaut, Michal & Wallace, Stein W., 2012. "Single-commodity network design with random edge capacities," European Journal of Operational Research, Elsevier, vol. 220(2), pages 394-403.
    14. Snoeck, André & Winkenbach, Matthias, 2020. "The value of physical distribution flexibility in serving dense and uncertain urban markets," Transportation Research Part A: Policy and Practice, Elsevier, vol. 136(C), pages 151-177.
    15. Wallace, Stein W. & Choi, Tsan-Ming, 2011. "Flexibility, information structure, options, and market power in robust supply chains," International Journal of Production Economics, Elsevier, vol. 134(2), pages 284-288, December.
    16. Rolf Golombek & Kjell Arne Brekke & Michal Kaut & Sverre A.C. Kittelsen & Stein W. Wallace, 2016. "Stochastic equilibrium modeling: The Impact of Uncertainty on the European Energy Market," EcoMod2016 9201, EcoMod.
    17. Julie Ann Stuart Williams & Randall Reid & Philip E. Billings & Natalie C. Belford, 2023. "Engaging Students in Optimization Modeling: Gaining Business Disruption Insights," INFORMS Transactions on Education, INFORMS, vol. 24(1), pages 85-94, September.
    18. Xin Wang & Teodor Gabriel Crainic & Stein W. Wallace, 2019. "Stochastic Network Design for Planning Scheduled Transportation Services: The Value of Deterministic Solutions," INFORMS Journal on Computing, INFORMS, vol. 31(1), pages 153-170, February.
    19. Curry, Stewart & Lee, Ilbin & Ma, Simin & Serban, Nicoleta, 2022. "Global sensitivity analysis via a statistical tolerance approach," European Journal of Operational Research, Elsevier, vol. 296(1), pages 44-59.
    20. Leung, Lawrence C. & Wong, Wai Hung & Hui, Yer Van & Wan, Yulai, 2013. "Managing third-party logistics under uncertainty: A decision scheme and managerial implications," International Journal of Production Economics, Elsevier, vol. 145(2), pages 630-644.
    21. Steffen Jaap Skotvoll Bakker & Jonas Martin & E. Ruben van Beesten & Ingvild Synn{o}ve Brynildsen & Anette Sandvig & Marit Siqveland & Antonia Golab, 2023. "STraM: A strategic network design model for national freight transport decarbonization," Papers 2304.14001, arXiv.org, revised Aug 2024.
    22. 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.
    23. Brekke, Kjell Arne & Golombek, Rolf & Kaut, Michal & Kittelsen, Sverre A.C. & Wallace, Stein W., 2017. "Stochastic energy market equilibrium modeling with multiple agents," Energy, Elsevier, vol. 134(C), pages 984-990.

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