Problem of grey bilevel linear programming and its algorithm

Based on the bilevel linear programming and the characteristic of grey system,a general gray bilevel linear programming problem with its model and theorem are given.A globally convergent algorithm based on simplex method is given to solve the drifting grey bilevel linear programming problem.Replacing the lower level problem by its Kuhn-Tucker condition,the gray bilevel linear programming is transformed into a gray single level programming problem,which can be transformed into a series of gray linear programming problem by use of the dual theory.So these problems can be solved by simplex method to obtain the solution of the gray bilevel linear programming problem.Finally,an example is adopted to verify the effectiveness of the proposed algorithm.