Inverse Stochastic Dominance and its Application in Production Process Control

  • Maciej Nowak
  • Tadeusz Trzaskalik
  • Grażyna Trzpiot
  • Kazimierz Zaraś
Conference paper
Part of the Advances in Soft Computing book series (AINSC, volume 12)


We are considering the problem of production process control in a firm, where a point to point type of production organisation is applied and production process control is held according to the Just-in-Time rule. In our paper we propose to solve the problem of production process control as a multiattribute problem. The algorithm, which we are proposing is built on a concept of outranking relation and inverse stochastic dominance. The multiattribute analysis, based on stochastic dominance, applies the utility theory to individual attributes in order to determinate a concordance level among them.


Decision Rule Stochastic Dominance Multiattribute Utility Alternative Pair First Degree Stochastic Dominance 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Arrow K. (1951). Social Choice and Individual Values. John Wiley and Sons, New York.Google Scholar
  2. 2.
    Arrow K. (1965). Aspects of the Theory of Risk Bearing. Yrjö Jahnssonin Säätio, Helsinki.Google Scholar
  3. 3.
    Bawa V.S., Linderberg E.B., Rafsky L.C. (1979). An Efficient Algorithm to Determine Stochastic Dominance Admissible Sets. Management Science, vol. 25, no. 7.Google Scholar
  4. 4.
    Goovaerts M.J. (1984). Insurance Premium. Elsevier Science. Publishers B. V.Google Scholar
  5. 5.
    Gravel M., Martel J.M., Nadeau R., Price W., Tremblay R. (1992). A multicriterion view of optimal resource allocation in job-shop production. European Journal of Operational Research 61, 230–244.CrossRefGoogle Scholar
  6. 6.
    Gravel M., Price W.L. (1988). Using the Kanban in job shop environment. International Journal of Production Research 26 /6, 1105–1118.CrossRefGoogle Scholar
  7. 7.
    Huang C.C., Kira D., Vertinsky I. (1978). Stochastic Dominance Rules for Multiattribute Utility Functions, Review of Economic Studies, vol. 41, 611–616.CrossRefGoogle Scholar
  8. 8.
    Kahneman D., Tversky A. (1979). Prospect theory: an analysis of decisions under risk. Econometrica 47, 262–291.CrossRefGoogle Scholar
  9. 9.
    Keeney R.L., Raiffa H. (1976). Decisions with Multiple Objectives: Preferences and Value Tradeoffs. Wiley.Google Scholar
  10. 10.
    Martel J.M., Zaras K. (1995). Une methode multicitere de rangement de projects face au risque. MS/OR Division, vol. 16, no. 2, 135–144.Google Scholar
  11. 11.
    Nowak M (1998) Wielokryterialna optymalizacja rozbudowy parku maszynowego. In: Modelowanie preferencji a ryzyko ‘88. AE Katowice.Google Scholar
  12. 12.
    Nowak M., Trzaskalik T., Zaras K. (1997). Dominacje stochastyczne i ich zastosowanie w analizie sterowania procesem produkcyjnym. In: Zarzadzanie przedsi@biorstwem XXI wieku. WSZMiJO Katowice, 255–264.Google Scholar
  13. 13.
    Roy B. (1985). Methodologie Multicriterie d’ Aide à la Décision. Economica, Paris.Google Scholar
  14. 14.
    Simon H.A. (1955). A Behaviour Model of Rational Choice. Quarterly Journal of Economics, 69, 99–118.CrossRefGoogle Scholar
  15. 15.
    Trzaskalik T., Trzpiot G., Zaras K (1998). Modelowanie preferencji z wykorzystaniem dominacji stochastycznych. AE KatowiceGoogle Scholar
  16. 16.
    Trzpiot G. (1997). Odwrotne dominacje stochastyczne. In: Zastosowania Badan Operacyjnych. Absolwent. f,ódz, 435–448.Google Scholar
  17. 17.
    Trzpiot G., Zaras K. (1999). Algorytm wyznaczania dominacji stochastycznych stopnia trzeciego. Badania Operacyjne i Decyzje 2 /1999, 7585.Google Scholar
  18. 18.
    Whitemore G. (1970). Third Stochastic Dominance American Economic Review, no. 60.Google Scholar
  19. 19.
    Zaras K. (1989). Dominance stochastique pour deux classes de fonctions d’utille: concaves et convexes. Rairo: Recherche operationnelle, no. 23.Google Scholar
  20. 20.
    Zaras K., Martel J.M. (1994). Multiattribute Analysis based on Stochastic Dominance In: Models and Experiments in Risk and Rationality Kluwer Academic Publishers, 225–248.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Maciej Nowak
    • 1
  • Tadeusz Trzaskalik
    • 1
  • Grażyna Trzpiot
    • 2
  • Kazimierz Zaraś
    • 3
  1. 1.Department of Operations ResearchThe Karol Adamiecki University of Economics in KatowiceKatowicePoland
  2. 2.Department of StatisticsThe Karol Adamiecki University of Economics in KatowiceKatowicePoland
  3. 3.Université du Québec en Abitibi-TemiscamingueRouyn-Noranda, QuébecCanada

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