The Game Algorithm Of Bilevel Programming

Because of the outstanding realistic background and extensive application, many researchers proceed thorough research to hierarchical system. It has been extensively applied in society economy, engineering technique, manage department and military etc. The research object of this paper is bilevel linear programming problem of hierarchical system. The main works are as follows:Firstly, the bilevel linear programming without constraint in the upper level is elaborated in the beginning. More over, the properties and relevant theorems of bilevel linear programming are discussed on a hypothetical condition.Secondly, game theory is applied to bilevel programming problem for a better illustration and soluntion of the bilevel linear programming problem. After knowing all extreme points of admissible set, we introduce membership function and produce fuzzy satisfactory degree of the upper level and the lower level programming in each extreme point, then use game theory to produce a finite two-person nonzero-sum bimatrix game in which the upper level and the lower level programming as players. According to some theory about Nash equilibrium theory, we get the satisfactory solution of the bilevel linear programming problem.Finally, due to its hierarchical structural characteristics, the optimal solution of bilevel programming, often regardless of lower level's interests, even at the expense of the lower level's interests, can not satisfied both the upper level and lower level decision makers simultaneously. Therefore, it is necessary to make the optimal solution effective. The Pareto effective solution could achieve mutual satisfaction, which requires the necessary cooperation between the two level decision makers. Enlightened by Nash bargaining models, we carry out a bargain over the optimal solution hold that hereby the obtained Nash bargaining solution is the Pareto efficient solution.