Research On The Methods Of Interval Linear Bi-level Programming

There are a lot of hierarchical decision-making problems in the field of economic management, which can be abstracted into hierarchical optimization models. Bilevel programming is a basic form of hierarchical optimization models. In order to describe uncertain hierarchical decision-making problems, some mathematic models such as fuzzy bilevel programming and stochastic bilevel programming are built by researchers, and the related modeling theory and algorithm are proposed. However, it is difficult for decision-makers to give the precise distribution functions or membership functions which are required in above methods. Since just only upper bound and lower bound are required, interval number is a simpler and commoner way to describe the uncertainty parameters, and interval programming has wider range of application. Sometimes, fuzzy programming and stochastic programming can be changed into interval programming. However, research on interval programming is focused on one-level programming. With the development of society and the expansion of economic globalization, hierarchy and uncertainty of decision-making problem become increasingly obvious. Therefore, the research on interval bilevel programming approach has a great significance. Based on the theory and methodology of one-level interval programming and bilevel programming, the solution concepts of interval linear bilevel programming are proposed and corresponding algorithms are designed under the specific decision-making background.The main work and innovation points of this thesis include: Firstly, for the interval linear bilevel programming model where all coefficients are intervals, the concept of optimal values interval is put forward, properties of optimal value interval is discussed, kth-best algorithm is designed to obtain the best optimal value, and two algorithms are proposed to estimate the upper bound and lower bound of the worst optimal value, respectively. Secondly, a new partial order on interval number is defined. Based on partial order and possibility degree on interval number,λ-Δsatisfactory solution of the interval programming is defined, and K-T condition forλ-Δsatisfactory solution is given; For interval linear bilevel programming model where all coefficients are intervals,λ-Δ1-Δ2 satisfactory solution is defined. Based on K-T condition,λ-Δ1-Δ2 satisfactory solution can be obtained by solving a two-objectives programming, and the model and method are applied to uncertainty distribution-purchasing decision-making.Thirdly, for the interval linear bilevel programming with interval coefficients in upper objective, minimax regret solution is defined based on minimax regret principle, its properties are presented, and a genetic algorithm is designed to find the minmax regret solution. For the interval linear bilevel programming model where all coefficients are interval, minimax regret solution based on reference set is proposed, and corresponding decision-making steps are given.Fourthly, for the interval linear bilevel programming with interval coefficients in lower objective, under the decision-making background of information asymmetry or information delay, optimism solution and pessimism solution are defined based on the decision maker's preference, properties of solutions are discussed, and a Branch and bound algorithm is proposed to find the optimism solution. When the information itself is uncertain, a new decision-making mechanism is presented, general concept of incentive function and incentive solution are defined, a specific incentive mechanism based on vertex and corresponding incentive solution are put forward, the kth-best is designed for calculating the solution based on solution's properties.