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Compromise programming with Tchebycheff norm for discrete stochastic orders

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  • Sebastian Sitarz

Abstract

This paper presents a method of decision making with returns in the form of discrete random variables. The proposed method is based on two approaches: stochastic orders and compromise programming used in multi-objective programming. Stochastic orders are represented by stochastic dominance and inverse stochastic dominance. Compromise programming uses the augmented Tchebycheff norm. This norm, in special cases, takes form of the Kantorovich and Kolmogorov probability metrics. Moreover, in the paper we show applications of the presented methodology in the following problems: projects selections, decision tree and choosing a lottery. Copyright The Author(s) 2013

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  • Sebastian Sitarz, 2013. "Compromise programming with Tchebycheff norm for discrete stochastic orders," Annals of Operations Research, Springer, vol. 211(1), pages 433-446, December.
    • Handle: RePEc:spr:annopr:v:211:y:2013:i:1:p:433-446:10.1007/s10479-013-1493-2
    DOI: 10.1007/s10479-013-1493-2
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    References listed on IDEAS

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    1. Sitarz, Sebastian, 2012. "Mean value and volume-based sensitivity analysis for Olympic rankings," European Journal of Operational Research, Elsevier, vol. 216(1), pages 232-238.
    2. Trzaskalik, Tadeusz & Sitarz, Sebastian, 2007. "Discrete dynamic programming with outcomes in random variable structures," European Journal of Operational Research, Elsevier, vol. 177(3), pages 1535-1548, March.
    3. Haim Levy, 1992. "Stochastic Dominance and Expected Utility: Survey and Analysis," Management Science, INFORMS, vol. 38(4), pages 555-593, April.
    4. Gass, Saul I. & Roy, Pallabi Guha, 2003. "The compromise hypersphere for multiobjective linear programming," European Journal of Operational Research, Elsevier, vol. 144(3), pages 459-479, February.
    5. Alison L. Gibbs & Francis Edward Su, 2002. "On Choosing and Bounding Probability Metrics," International Statistical Review, International Statistical Institute, vol. 70(3), pages 419-435, December.
    6. Sitarz, Sebastian, 2008. "Postoptimal analysis in multicriteria linear programming," European Journal of Operational Research, Elsevier, vol. 191(1), pages 7-18, November.
    7. Darinka Dentcheva & Andrzej Ruszczynski, 2005. "Inverse stochastic dominance constraints and rank dependent expected utility theory," GE, Growth, Math methods 0503001, University Library of Munich, Germany.
    8. Nowak, Maciej, 2007. "Aspiration level approach in stochastic MCDM problems," European Journal of Operational Research, Elsevier, vol. 177(3), pages 1626-1640, March.
    9. Sebastian Sitarz, 2010. "Standard sensitivity analysis and additive tolerance approach in MOLP," Annals of Operations Research, Springer, vol. 181(1), pages 219-232, December.
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    1. Ana Garcia-Bernabeu & Antonio Benito & Mila Bravo & David Pla-Santamaria, 2016. "Photovoltaic power plants: a multicriteria approach to investment decisions and a case study in western Spain," Annals of Operations Research, Springer, vol. 245(1), pages 163-175, October.

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