| Classical research works for stochastic integer programming problem are obtained by the basic assumption of the completely known probability distribution. However, in many situations, the decision-maker can only get partial information of probability distribution, and one cannot determine the exact values of the probability for the occurrence of random events due to insufficient historical data and limited statistical method. As a common case, the information of the probability distribution are generally determined by integrating the experience of the experts, and a broad range of the probability which can be described as fuzzy number is only obtained.Stochastic integer programming problem in which the probabilities of random events are fuzzy numbers is studied in this thesis. The structural properties for two-stage stochastic inter programming with recourse under fuzzy stochastic probability distribution are discussed. α-cut technology is used to transform fuzzy equalities or inequalities into deterministic equalities or inequalities, and the two-stage stochastic integer programming model is established by making use of minmax rule. On this basis, the integer L-shaped algorithm is developed to solve the problem. Finally, we give the example of the farmer’s problem in order to illustrate the algorithm process in this thesisThe main work of the study is as follows:Firstly, two-stage stochastic integer programming model and the solving algorithm under fuzzy probability distribution is established by using minmax rule. Secondly, some structural properties for the two-stage stochastic ineger programming with recourse under fuzzy stochastic probability distribution are discussed. Thirdly, the example of the farmer’s problem is given to illustrate the algorithm process in this thesis. |
