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Chance Constrained Programming with one Discrete Random Variable in Each Constraint

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  • Emilio Cerdá
  • Julio Moreno Lorente

Abstract

Stochastic programming problems in which there are linear constraints containing one discrete random variable among either the technical coefficients or the resource (which are all positive), and non-negativity constraints for the variables, are studied. First, the case of just one linear constraint with stochastic resource is presented. Next is the case of just one linear constraint where one of the technical coefficients is a random variable. In both cases, initially the case of two decision variables is studied, which permits us to solve the problems taking advantage of the corresponding graphical representations. The corresponding generalizations for the case of n decision variables follow. The general case of several of such constraints is also presented. All the specific solution methods obtained are based on the chance constrained method. Each of the cases is illustrated with an example taken from Economics.

Suggested Citation

  • Emilio Cerdá & Julio Moreno Lorente, 2009. "Chance Constrained Programming with one Discrete Random Variable in Each Constraint," Working Papers 2009-05, FEDEA.
    • Handle: RePEc:fda:fdaddt:2009-05
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    References listed on IDEAS

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    3. R. Caballero & E. Cerda & M. Muñoz & L. Rey, 2002. "Analysis and comparisons of some solution concepts for stochastic programming problems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 10(1), pages 101-123, June.
    4. Stein W. Wallace & Stein-Erik Fleten, 2002. "Stochastic programming in energy," GE, Growth, Math methods 0201001, University Library of Munich, Germany, revised 13 Nov 2003.
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