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.

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.