Study Of Stochastic Convex Programming With Fuzzy Probability Distribution And Its Application

The research of two-stage and multi-stage stochastic linear programming has made great development, the research results of the theory and method are mostly based on the basic hypothesis that probability distribution is fully known. But in many cases, the probability distribution of random variable cannot be fully known. Recently, Abdelaziz and Masri built the two-stage and multi-stage stochastic linear programming with fuzzy probability distribution, and gave the solving algorithm. Considering the reality application, a lot of the research objects are nonlinear. Based on the theory above, two-stage and multi-stage stochastic convex programming with fuzzy probability distribution, as well as solving algorithm, are studied in this paper. In the first step, the fuzzy transformation step, we utilized the a-cut technique to defuzzify the fuzzy equalities and fuzzy inequalities on the probability distribution. In the second step, the stochastic transformation step, we establish the certain equivalent model of stochastic convex programming with fuzzy probability distribution, according to the min-max principle. This paper presents L-shaped algorithm to solve two-stage and multi-stage stochastic convex programming with fuzzy probability distribution. Two numerical examples demonstrate the feasibility and efficiency for the model and solution. Finally, a bidding strategies model and the solving algorithm for generation companies under fuzzy probability distribution are developed, and the calculation results are compared with that classical stochastic programming.The main work in this paper includes the following four aspects:First, it establishes the two-stage stochastic convex programming with fuzzy probability distribution, and gives L-shaped algorithm to solve the program. Second, the multi-stage stochastic convex programming with fuzzy probability distribution is established, and L-shaped algorithm to solve the program is given. Third, this paper gives and proves the convergence theorem of designed L-shaped algorithm, the numerical examples show the essential characteristics of algorithm. Fourth, this paper gives the bidding strategy mode of power generation companies with fuzzy probability distribution, and an example is given to illustrate the reasonable and effective of method.