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Overview of Different Approaches for Solving Stochastic Programming Problems with Multiple Objective Functions

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Stochastic Versus Fuzzy Approaches to Multiobjective Mathematical Programming under Uncertainty

Part of the book series: Theory and Decision Library ((TDLD,volume 6))

Abstract

Stochastic programming is one of the most exciting and challenging developments of mathematical programming. It aims to treat uncertainty within decision oriented models in a coherent and systematic way. Lack of such an approach is one of the objections raised to deterministic mathematical programming modelling. The requirement for a single objective or payoff functions is another objection; it can be argued that most decision makers usually have several decision criteria, and multi-objective programming aims to reflect this. Also simple examples show (similar to the Endorsed paradox and Arrow impossibility theorems) that there are, in general, no good ways of aggregating several criteria into one objective function. But maybe sometimes there are. Worse, even when there is a natural objective function, but stochastic elements come into play maximizing the expectation will often involve unacceptable large variances. In this way, a new interdisciplinary science is about to be born-stochastic programming with several objective functions.

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  1. Laboratories of the Department of Economic Cybernetics, Calea Dorobanţi 15–17, 71131, Bucharest, Romania

    I. M. Stancu-Minasian

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  1. I. M. Stancu-Minasian
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  1. Technical University of Poznan, Poznan, Poland

    Roman Slowinski

  2. Faculté Polytechnique de Mons, Mons, Belgium

    Jacques Teghem

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Stancu-Minasian, I.M. (1990). Overview of Different Approaches for Solving Stochastic Programming Problems with Multiple Objective Functions. In: Slowinski, R., Teghem, J. (eds) Stochastic Versus Fuzzy Approaches to Multiobjective Mathematical Programming under Uncertainty. Theory and Decision Library, vol 6. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-2111-5_5

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  • DOI: https://doi.org/10.1007/978-94-009-2111-5_5

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  • Online ISBN: 978-94-009-2111-5

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