FUZZY APPROACH FOR MULTILEVEL PROGRAMMING-PROBLEMS

Multi-level programming techniques are developed to solve decentralize d planning problems with multiple decision makers in a hierarchical or ganization. These become more important for contemporary decentralized organizations where each unit or department seeks its own interests. Traditional approaches include vertex enumeration and transformation a pproaches. The former is in search of a compromise vertex based on adj usting the control variable(s) of the higher level and thus is rather inefficient. The latter transfers the lower-level programming problem to be the constraints of the higher level by its Kuhn-Tucker condition s or penalty function; the corresponding auxiliary problem becomes non -linear and the decision information is also implicit. In this study, we use the concepts of tolerance membership functions and multiple obj ective optimization to develop a fuzzy approach for solving the above problems. The upper-level decision maker defines his or her objective and decisions with possible tolerances which are described by membersh ip functions of fuzzy set theory. This information then constrains the lower-level decision maker's feasible space. A solution search relies on the change of membership functions instead of vertex enumeration a nd no higher order constraints are generated. Thus, the proposed appro ach will not increase the complexities of original problems and will u sually solve a multilevel programming problem in a single iteration. T o demonstrate our concept, we have solved numerical examples and compa red their solutions with classical solutions.