Annals of Operations Research

, Volume 51, Issue 1, pp 45–59 | Cite as

PROMISE: A DSS for multiple objective stochastic linear programming problems

  • Raymond Nadeau
  • Bruno Urli
  • Laszlo N. Kiss
Multicriteria Decision Making Support

Abstract

Most of the multiple objective linear programming (MOLP) methods which have been proposed in the last fifteen years suppose deterministic contexts, but because many real problems imply uncertainty, some methods have been recently developed to deal with MOLP problems in stochastic contexts. In order to help the decision maker (DM) who is placed before such stochastic MOLP problems, we have built a Decision Support System called PROMISE. On the one hand, our DSS enables the DM to identify many current stochastic contexts: risky situations and also situations of partial uncertainty. On the other hand, according to the nature of the uncertainty, our DSS enables the DM to choose the most appropriate interactive stochastic MOLP method among the available methods, if such a method exists, and to solve his problem via the chosen method.

Keywords

Multiple objective linear programming stochastic decision support system 

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References

  1. [1]
    R. Benayoun, J. de Montgolfier, J. Tergny and O. Larichev, Linear programming and multiple objective functions: STEP method (STEM), Math. Progr. 1(1971)366–375.CrossRefGoogle Scholar
  2. [2]
    A.M. Geoffrion, J.S. Dyer and A. Feinberg, An interactive approach for multicriterion optimization with an application to the operation of an academic department, Manag. Sci. 19(1972)357–368.Google Scholar
  3. [3]
    A. Goicoechea, D.R. Hansen and L. Duckstein,Multiobjective Decision Analysis with Engineering and Business Applications (Wiley, New York, 1982).Google Scholar
  4. [4]
    P. Kall,Stochastic Linear Programming (Springer, Berlin, 1976).Google Scholar
  5. [5]
    G. Klein, H. Moskowitz and A. Ravindran, Interactive multiobjective optimization under uncertainty, Manag Sci. 36(1990)58–75.CrossRefGoogle Scholar
  6. [6]
    R. Slowinsky and J. Teghem (eds.),Stochastic versus Fuzzy Approach to Multiobjective Mathematical Programming Under Uncertainty (Kluwer Academic, Dordrecht, 1990).Google Scholar
  7. [7]
    I.M. Stancu-Minasian,Stochastic Programming with Objective Functions (D. Reidel, Dordrecht, 1984).Google Scholar
  8. [8]
    J. Teghem, Multiobjective linear programming under different scenarios, communication atEuro XII/TIMS 21st Meeting, Helsinki (1992).Google Scholar
  9. [9]
    J. Teghem, D. Dufrane, M. Thauvoye and P. Kunsh, STRANGE: an interactive method for multiobjective linear programming under uncertainty, Eur. J. Oper. Res. 26(1986)65–82.CrossRefMathSciNetGoogle Scholar
  10. [10]
    B. Urli and R. Nadeau, Multiobjective stochastic linear programming with incomplete information: a general methodology, in:Stochastic versus Fuzzy Approaches to Multiobjective Mathematical Programming Under Uncertainty, ed. R. Slowinsky and J. Teghem, op.cit. (1990).Google Scholar
  11. [11]
    B. Urli and R. Nadeau, Stochastic MOLP with incomplete information: an interactive approach with recourse, J. Oper. Res. Soc. 41(1990)1143–1152.Google Scholar
  12. [12]
    B. Urli and R. Nadeau, An interactive method to multiobjective linear programming problems with interval coefficients, INFOR 30(1992)127–137.Google Scholar
  13. [13]
    B. Urli and R. Nadeau, Scenarios based interactive methods for multiobjective stochastic linear programming, Cahiers de recherche de l'Université du Québec à Rimouski (1993).Google Scholar
  14. [14]
    H.J. Zimmermann, L.A. Zadeh and R.B. Gaines (eds.),Fuzzy Sets and Decision Analysis (North-Holland, Amsterdam, 1984).Google Scholar

Copyright information

© J.C. Baltzer AG, Science Publishers 1994

Authors and Affiliations

  • Raymond Nadeau
    • 1
  • Bruno Urli
    • 2
  • Laszlo N. Kiss
    • 1
  1. 1.Sciences de l'administrationUniversité LavalCanada
  2. 2.Université du Québec à RimouskiCanada

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