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An interactive method of tackling uncertainty in interval multiple objective linear programming

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Abstract

Mathematical programming models for decision support must explicitly take account of the treatment of the uncertainty associated with the model coefficients along with multiple and conflicting objective functions. Interval programming just assumes that information about the variation range of some (or all) of the coefficients is available. In this paper, we propose an interactive approach for multiple objective linear programming problems with interval coefficients that deals with the uncertainty in all the coefficients of the model. The presented procedures provide a global view of the solutions in the best and worst case coefficient scenarios and allow performing the search for new solutions according to the achievement rates of the objective functions regarding both the upper and lower bounds. The main goal is to find solutions associated with the interval objective function values that are closer to their corresponding interval ideal solutions. It is also possible to find solutions with non-dominance relations regarding the achievement rates of the upper and lower bounds of the objective functions considering interval coefficients in the whole model.

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References

  1. R. Benayoun, J. de Montgolifer, J. Tergny, and O. Larichev, “Linear programming and multiple objective functions: STEP method (STEM),” Math. Programming, 1, No. 3, 366–375 (1971).

    Article  MATH  MathSciNet  Google Scholar 

  2. G. G. Brown and G. W. Graves, Elastic Programming: A New Approach to Large – Scale Mixed Integer Optimization, ORSA TIMS, Las Vegas (1975).

    Google Scholar 

  3. J. W. Chinneck and E. W. Dravnieks, “Locating minimal infeasible constraint sets in linear programs,” ORSA J. Comput., 3, No. 2, 57–168 (1991).

    Google Scholar 

  4. J. W. Chinneck and K. Ramadan, “Linear programming with interval coefficients,” J. Oper. Res. Soc., 51, 209–220 (2000).

    Article  MATH  Google Scholar 

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

  6. M. Inuiguchi and Y. Kume, “Goal programming problems with interval coefficients and target intervals,” Eur. J. Oper. Res., 52, 345–360 (1991).

    Article  MATH  Google Scholar 

  7. K. G. Murty, S. N. Kabadi, and R. Chandrasekarn, “Infeasibility analysis for linear systems. A survey,” Arabian J. Sci. Eng., 25, (1C), 3–18 (2000).

    Google Scholar 

  8. C. Oliveira and C. H. Antunes, “Multiple objective linear programming models with interval coefficients – an illustrated overview,” Eur. J. Oper. Res., 181, 1434–1463 (2007).

    Article  MATH  Google Scholar 

  9. T. Shaocheng, “Interval number and fuzzy number linear programming,” Fuzzy Sets Syst., 66, 301–306 (1994).

    Article  Google Scholar 

  10. A. Sengupta and K. Pal, “On comparing interval numbers,” Eur. J. Oper. Res., 127, 28–43 (2000).

    Article  MATH  MathSciNet  Google Scholar 

  11. B. Urli and R. Nadeau, “An interactive method to multiobjective linear programming problems with interval coefficients,” INFOR, 30, No. 2, 127–137 (1992).

    MATH  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  13. F. R. Wondolowski, “A generalization of Wendell’s tolerance approach to sensitivity analysis in linear programming,” Decision Sci., 22, 792–810 (1991).

    Article  Google Scholar 

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Authors and Affiliations

  1. Inesc Coimbra, Coimbra, Portugal

    C. Oliveira

  2. Universidade de Coimbra, Coimbra, Portugal

    C. H. Antunes

Authors
  1. C. Oliveira
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  2. C. H. Antunes
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Correspondence to C. Oliveira.

Additional information

Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 63, Optimal Control, 2009.

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Oliveira, C., Antunes, C.H. An interactive method of tackling uncertainty in interval multiple objective linear programming. J Math Sci 161, 854–866 (2009). https://doi.org/10.1007/s10958-009-9606-9

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  • DOI: https://doi.org/10.1007/s10958-009-9606-9

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