Decentralized planning has long been recognized as an important decision making problem. Many approaches based on the concepts of large-scale system decomposition have generally lacked the ability to model the type of truly independent subsystem which often exist in practice. Multilevel PROGRAMMING models partition control over decision variable among ordered levels within a hierarchical planning structure. This paper examines the special case of the multilevel liner PROGRAMMING problem, i.e. BILEVEL linear PROGRAMMING problem. BILEVEL PROGRAMMING often represent an adequate tool for modeling non cooperative hierarchical decision processes, where one player optimizes over a subset of decision variables, while taking into account the independent reaction of the other player to his or course of action. BILEVEL PROGRAMMING is an important area of current research stimulated by it's intrinsically very difficult nature and is still a little known technique, rarely used despite all it's potential capabilities. in this note a definition for a general BILEVEL PROGRAMMING some applications, geometric characterization and solution approaches are presented with some examples.

BILEVEL linear PROGRAMMING is a decision making problem with a two-level decentralized organization. The “leader” is in the upper level and the “follower”, in the lower. Making a decision at one level affects that at the other one. In this paper, BILEVEL linear PROGRAMMING with inexact parameters has been studied and a method is proposed to solve a fuzzy BILEVEL linear PROGRAMMING using interval BILEVEL linear PROGRAMMING.

BILEVEL PROGRAMMING, a tool for modeling decentralized decision problem, consists of the objective of the leader at its first level and that of the follower at the second level. BILEVEL PROGRAMMING has been proved to be Np hard problem. Numerous algorithms have been developed for solving BILEVEL PROGRAMMING problem. These algorithms have not enough efficiency for solving a real problem. In this paper an attempt has been made to develop an algorithm based on Tabu Search (TS) approach. This algorithm can be efficient to finding a near optimal solution. In this paper, the proposed method and that of Mathieu and et.al [1] are also compared by solving different problems.

BILEVEL PROGRAMMING, a tool for modeling decentralized decision problem, consists of the objective of the leader at its first level and that of the follower at the second level. BILEVEL PROGRAMMING has been proved to be an Np-hard problem. Numerous algorithms have been developed for solving BILEVEL PROGRAMMING problems. These algorithms lack the required efficiency for solving a real problem. In this paper, attempts have been made to develop an algorithm based Simulated Annealing (SA) Approach. This algorithm is efficient enough to find a near optimal solution. The proposed method is compared with the one developed by Mathieu et al [1] through application of both to a number of different problems.  

In sciences and industries such as signal optimization, traffic assignment, economic market and etc, many problems have been modeled by BILEVEL PROGRAMMING (BLP) problems, where in each level one must optimize some objective functions. There are so many algorithms in order to find the global optimum of the linear version of BLP problems. This paper addresses multi-objective linear BILEVEL multi-follower PROGRAMMING (MOLBMFP) problems in which there is no sharing information among followers. It presents a new method for solving these problems.