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On multiparametric analysis in network linear programming

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Abstract

In this paper, we study multiparametric sensitivity analysis in network linear programming problem using the concept of maximum volume within tolerance region. We construct critical regions for simultaneous and independent perturbations in the objective function coefficients and in the right-hand-side vector of the given network linear program. Necessary and sufficient conditions are derived to classify the parameters as ‘focal’ and ‘nonfocal’. Nonfocal parameters can have unlimited variations and hence, because of their low sensitivity in practice, they are deleted from the analysis. For focal parameters, a maximum volume tolerance region is characterized. Theoretical results are illustrated with the help of numerical example.

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References

  1. Ahuja, R.K., Magnanti, T.L and Orlin, J.B. (1980). Network Flows: Theory, Algorithms and Applications, Prentice Hall, Englewood Cliffs, New Jersey.

  2. Gal, T. (1979). Postoptimal Analysis, Parametric Programming and Related Topics, McGraw-Hill, New York.

    Google Scholar 

  3. Liebman, J., Ladson, L., Scharge, L., and Waren, A. (1986), “Modeling and optimization with GINO”, The Scientific Press, San Francisco, CA.

    Google Scholar 

  4. Ravi, N., and Wendell, R.E. (1988). “The tolerance approach to sensitivity analysis in network linear programming”, Networks, Vol. 18, 159–171.

    Article  Google Scholar 

  5. Wang, H.F., and Huang, C.S. (1992). “The maximal tolerance analysis of the constraint matrix in linear programming”, Journal of Chinese Institute of Engineers, Vol. 15, No.5, pp.507–517.

    Article  Google Scholar 

  6. Wang, H.F., and Huang, C.S. (1993). “Multi-parametric analysis of the maximum tolerance in a linear programming problem”, European Journal of Operational Research, Vol. 67, 75–87.

    Article  Google Scholar 

  7. Wendell, R.E. (1982). “A preview of a tolerance approach to sensitivity analysis in linear programming”, Discrete Mathematics, Vol. 38, 121–124.

    Article  Google Scholar 

  8. Wendell, R.E. (1984). “Using bounds on the data in linear programming: The tolerance approach to sensitivity analysis”, Mathematical Programming, Vol. 29, 304–322.

    Article  Google Scholar 

  9. Wendell, R.E. (1985). “The tolerance approach to sensitivity analysis in linear programming”, Management Science, Vol. 31, 564–578.

    Article  Google Scholar 

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Authors and Affiliations

  1. Scientific Analysis Group, DRDO, Ministry of Defence, Metcalfe House, 110054, Delhi, India

    Sanjeet Singh

  2. Department of Mathematics, Deen Dayal Upadhyaya College, Shivaji Marg, 110015, Karampura, New Delhi, India

    Pankaj Gupta

  3. Department of Operational Research, Faculty of Mathematical Sciences, University of Delhi, 110007, Delhi, India

    Davinder Bhatia

Authors
  1. Sanjeet Singh
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  2. Pankaj Gupta
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  3. Davinder Bhatia
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Singh, S., Gupta, P. & Bhatia, D. On multiparametric analysis in network linear programming. OPSEARCH 41, 237–249 (2004). https://doi.org/10.1007/BF03398847

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  • DOI: https://doi.org/10.1007/BF03398847

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