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Optimization of a linear function over the set of stochastic efficient solutions

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  • Chaabane Djamal
  • Mebrek Fatma

Abstract

In this paper we study the problem of optimization over an integer efficient set of a Multiple Objective Integer Linear Stochastic Programming problem. Once the problem is converted into a deterministic one by adapting the $$2$$ -levels recourse approach, a new pivoting technique is applied to generate an optimal efficient solution without having to enumerate all of them. This method combines both techniques, the L-shaped method and the combined method developed in Chaabane and Pirlot (J Ind Manag Optim 6:811–823, 2010 ). A detailed didactic example is given to illustrate different steps of our algorithm. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Chaabane Djamal & Mebrek Fatma, 2014. "Optimization of a linear function over the set of stochastic efficient solutions," Computational Management Science, Springer, vol. 11(1), pages 157-178, January.
    • Handle: RePEc:spr:comgts:v:11:y:2014:i:1:p:157-178
    DOI: 10.1007/s10287-012-0155-1
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    References listed on IDEAS

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    1. Peter Kall & János Mayer, 2005. "Stochastic Linear Programming," International Series in Operations Research and Management Science, Springer, number 978-0-387-24440-2, December.
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    3. Caballero, Rafael & Cerda, Emilio & del Mar Munoz, Maria & Rey, Lourdes, 2004. "Stochastic approach versus multiobjective approach for obtaining efficient solutions in stochastic multiobjective programming problems," European Journal of Operational Research, Elsevier, vol. 158(3), pages 633-648, November.
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    6. Sylva, John & Crema, Alejandro, 2007. "A method for finding well-dispersed subsets of non-dominated vectors for multiple objective mixed integer linear programs," European Journal of Operational Research, Elsevier, vol. 180(3), pages 1011-1027, August.
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