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Sensitivity Analysis in Multiple Objective Linear Programming: Changes in the Objective Function Matrix

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Multiple Criteria Decision Making Theory and Application

Part of the book series: Lecture Notes in Economics and Mathematical Systems ((LNE,volume 177))

Abstract

Changes or probable errors in input data in a Multiple Objective Linear Program raise the following question: What are the limits within which parameters can be varied without affecting the solution?

Sensitivity analysis enables the analyst to obtain answers which, otherwise, can be obtained only by formulating and solving different problems repeatedly. In this paper we address the problem of changes in the Objective Function Matrix and propose a solution method.

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References

  1. Belenson, S. M. and Kapur, K. C., “An Algorithm for Solving Multicriterion Linear Programming Problems with Examples”, Operational Research Quarterly, Vol. 24 (1973), pp. 65–77.

    Article  Google Scholar 

  2. Benayoun, R., de Montgolfier, J., Tergny, J. and Laritchev, O., “Linear Programming with Multiple Objective Functions: Step Method (STEM)” Mathematical Programming, Vol. 1 (1971), pp. 366–375.

    Article  Google Scholar 

  3. Da Cunha, N. D. and Ploak, E., “Constrained Minimization Under Vector Valued Criteria in Finite Dimensional Space”, Journal of Mathematical Analysis and Applications, Vol. 19 (1967), pp. 103–124.

    Article  Google Scholar 

  4. Deshpande, D. V., “Investigations in Multiple Objective Linear Programming—Theory and an Application”, Doctoral Dissertation in Progress, School of Management, SUNY Buffalo, (1979).

    Google Scholar 

  5. Deshpande, D. V. and Zionts, S., “Sensitivity Analysis in Multiple Ovjective Linear Programming”, Working Paper, School of Management, SUNY Buffalo, (1979).

    Google Scholar 

  6. Ecker, J. G. and Kouada, I. A., “Finding All Efficient Extreme Points for Linear Multiple Objective Programs”, Mathematical Programming, Vol. 14 (1978), pp. 249–261.

    Article  Google Scholar 

  7. Evans, J. P. and Steuer, R. E., “A Revised Simplex Method for Linear Multiple Objective Programs”, Mathematical Programming, Vol. 15 (1973), pp. 54–72.

    Article  Google Scholar 

  8. Gal, T., “A General Method for Determining the Set of All Efficient Solutions to a Linear Vector-maximum Problem”, Institut für Wirtschaftswissenschaften, Aachen, September 1976.

    Google Scholar 

  9. Gal, T. and Leberling, H., “Relaxation Analysis in Linear Vector Valued Optimization”, Institut für Wirtschaftswissenschaften, Aachen, Working Paper No. 76-15, November 1976.

    Google Scholar 

  10. Geoffrion, A. M., “Proper Efficiency and the Theory of Vector Maximization”, Journal of Mathematical Analysis and Applications, Vol. 22 (1968), pp. 618–630.

    Article  Google Scholar 

  11. Gillmore, P. C, and Gomory, R. E., “A Linear Programming Approach to the Culting Stock Problem, Part II.”, Operations Research, Vol. 11 (1963), pp. 863–888.

    Article  Google Scholar 

  12. Hegner, N. S., “Multiple Objective Linear Programming”, Unpublished Doctoral Dissertation, Rensselaer Polytechnic Institute, 1977.

    Google Scholar 

  13. Isermann, H., “The Enumeration of the Set of All Efficient Solutions for a Linear Multiple Objective Program”, Operational Research Quarterly, Vol. 28 (1977), pp. 711–725.

    Article  Google Scholar 

  14. Kornbluth, J. S. H., “Duality, Indifference and Sensitivity Analysis in Multiple Objective Linear Programming”, Operational Research Quarterly, Vol. 25 (1974), pp. 519–614.

    Article  Google Scholar 

  15. Philip, J., “Algorithms for the Vector Maximization Problem”, Mathematical Programming, Vol. 2 (1972), pp. 207–229.

    Article  Google Scholar 

  16. Thompson, G. L., Tonge, F. M., and Zionts, S., “Techniques for Removing Nonbinding Constraints and Extraneous Variables from Linear Programming Problems”, Management Science, Vol. 12 (1966), pp. 588–608.

    Article  Google Scholar 

  17. Zeleny, M., “Linear Multiobjective Programming”, New York, Springer — Verlag, 1974.

    Book  Google Scholar 

  18. Zionts, S., “Size Reduction Techniques in Linear Programming and Their Applications”, Unpublished Doctoral Dissertation, Carnegie-Mellon University, 1965.

    Google Scholar 

  19. Zionts, S. and Wallenius, J., “An Interactive Programming Method for Solving the Multiple Criteria Problem”, Management Science, Vol. 22 (1976), pp. 652–663.

    Article  Google Scholar 

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© 1980 Springer-Verlag Berlin Heidelberg

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Deshpande, D.V., Zionts, S. (1980). Sensitivity Analysis in Multiple Objective Linear Programming: Changes in the Objective Function Matrix. In: Fandel, G., Gal, T. (eds) Multiple Criteria Decision Making Theory and Application. Lecture Notes in Economics and Mathematical Systems, vol 177. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-48782-8_3

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  • DOI: https://doi.org/10.1007/978-3-642-48782-8_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09963-5

  • Online ISBN: 978-3-642-48782-8

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