Two-stage Programming Problems In Birandom Environment

In this thesis, based on birandom theory, a new class of two-stage birandom programming model is proposed, and some mathematical properties of the model are also studied. In the case of general recourse matrix, we discuss the convexity of feasible set and the convexity of the objective function; In the case of complete recourse matrix, we prove the continuity and the differentiability of the objective. In addition, three solution concepts which are related to this birandom programming model are presented, they are distribution solution, recourse solution and expected value solution. Based on the three solution concepts, two important indexes, the value of birandom solution and the expected value of perfect information are defined, and their relations are also studied.The major new results can be summarized as follows:· Two-stage birandom programming model is proposed, which generalizes random optimization theory;· The convexity of feasible set, and the convexity, the continuity and the differentiability of the objective function are studied;· Three solution concepts which are related to birandom programming are defined, and their relations are discussed.