Skip to main content

Linear Programming with Uncertain Data: Some Extensions to Robust Optimization


An optimization problem often has some uncertain data, and the optimum of a linear program can be very sensitive to small changes in the data. Such a problem can often be modified to a robust program, which is more stable to such changes. Various methods for this are compared, including requiring all versions of the data to be satisfied together (but they may be inconsistent), worst-case MAX–MIN model, and various models where deviations incur penalty costs. Existing methods require substantial computation. It is shown here that smaller computations often suffice; not all cases need be considered. Other penalty methods are suggested, using different norms. Moreover, perturbations of constraint coefficients can be represented by suitable perturbations of a requirement vector.

This is a preview of subscription content, access via your institution.


  1. Ravindran, A., Ravi, A.: Robust optimization. In: Greenberg, H.J., Morrison, T. (eds.) Operations Research Methodologies. CRC, Hoboken (2008)

    Google Scholar 

  2. Ben-Tal, A., El Ghaoui, L., Nemirovski, A.: Robust Optimization. Princeton University Press, Princeton (2009)

    MATH  Google Scholar 

  3. Kouvelis, P., Gang, Y.: Robust Discrete Optimization and Its Applications. Kluwer, Dordrecht (2010)

    Google Scholar 

  4. Mulvey, J.M., Vanderbei, R.J.: Robust optimization of large-scale systems. Oper. Res. 41(2), 264–281 (1995)

    Article  MathSciNet  Google Scholar 

  5. Ruczczyński, Shapiro (eds.): Stochastic Programming. Elsevier, Amsterdam (2000)

    Google Scholar 

  6. Tapiero, C.S.: Applied Stochastic Models and Control for Finance and Insurance. Kluwer, Dordrecht (1998)

    Book  MATH  Google Scholar 

  7. Dupačová, Stepan, J.: Stochastic Modeling in Economics and Finance. Kluwer, Dordrecht (2002)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to B. D. Craven.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Craven, B.D., Islam, S.M.N. Linear Programming with Uncertain Data: Some Extensions to Robust Optimization. J Optim Theory Appl 155, 673–679 (2012).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: