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Multistage stochastic programming with fuzzy probability distribution 

Abstract: In this paper, we study stochastic programs with partial information on probability distribution (SPI) [1,2]. The probability distribution is discrete and is only known to belongs to a given polyhedral set. Stochastic programs with moment constraints in the probability distribution represent a special case of SPI problem.
We extend the solution method for the two stage case [3], to solve the multistage SPI program. First, a certainty equivalent is constructed using the hypothesis that the Decision Maker (DM) has a pessimistic attitude and then the resulting program is solved using a modified version of the nested L-shaped method.

Keywords: Stochastic programming, Partial linear information, Multistage stochastic programming, Nested L-shaped decomposition method.

[1] P. Abel (1987) Stochastic linear programming with recourse under partial information, in Probability and Bayesian statistics (Innsbruck, 1986), Plenum, New York, pp.1-6.

[2] F. Ben Abdelaziz and H. Masri (2000): Linear programming under uncertainty: a chance constrained approach, in the proceedings of the international conference ACIDCA' 2000, 22-24 March 2000.

[3] F. Ben Abdelaziz and H. Masri (2001): Stochastic programming with fuzzy probability distribution, Submitted in the proceeding of the SCRO-JOPT conference, Mai 2001.