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.