Two-Stage Stochastic Convex Programming with Linear Partial Information

Stochastic programming has already been applied to very broad fields. It is necessary in the solution of the model that the complete information about the probability distribution is known by decision makers. However, in many practical situations, this request could not be met by the limiting statistics and the incomplete historic data. A new decision making method named stochastic linear programming with linear partial information about probability distribution (SLPLPI) was recently proposed by Abdelaziz et al.(2005). As an improvement, in this paper, we extend that work from the stochastic linear programming to the stochastic convex programming. One two-stage stochastic convex programming with linear partial information about the probability distribution (SCPLPI) is modeled by maximizing the expected minimal value (MaxEmin). We make use of Lagrangian duality theorem instead simplex method of stochastic linear programming to develop a new solution method. An improved L-shaped algorithm is developed for solving the stochastic convex programming. The convergence theorem of the algorithm is confirmed. Finally, a numerical example illustrates the essential of the method proposed.