The Problem Of Grey Bilievel Linear Programming And Its Algorithm

The hierarchical system is main form of society organized management, multilevel programming is fundamental model used to study this kind of systematical problem. Because of its outstanding realistic background and the extensive application prospects, many researchers proceed thorough research to the hierarchical system. It has been extensively applied in society economy, engineering technique, manage department and military etc. The grey resources distribute problem and interval type price control problem of grey bilevel linear programming are mainly studied in the paper. Details are as follows:Firstly, bilevel linear programming is divided into resources distribute problem, price control problem and general bilevel linear programming, their basic model, definition and theorem are given and the interrelated properties are discussed respectively under different hypothesis.Secondly, the theory of grey system is induced. Its characteristic, basic concept, basic theorem, and the algorithm are briefly introduced. The problem of grey linear programming is made a summary and the problem of drifting grey linear programming is detailedly summarized which make the essential preparative of theoretics for advancing the problem of grey bilevel linear programming.Finally, problem of grey bilevel linear programming is divided into grey resources distribute problem and interval type price control problem and their basic model, definition and theorem is given in the paper. A globally convergent algorithm without reliability based on simplex method is given to solve the drifting grey bilevel linear programming problem which is more availability in the calculating precision compared with traditional reliability algorithm. An interval number pleased degree algorithm combined with penalty function is given to solve the interval type price control problem by defining a new pleased degree and an example is adopted to verify the effectiveness of the proposed algorithm.