Bilevel Programming and Recent Approaches

Decentralized planning has long been recognized as an important decision makingProblem Many approaches based on the concepts of large-scale system decomposition have generallylacked the ability to model the type of truly independent subsystems which often exist inpractice. Multilevel programming models partition control over decision variables amongordered levels within a hierarchical planning structure. This paper examines the special caseof the multilevel linear programming problem, i.e, bilevel linear programming problem.Bilevel programming often represents an adequate tool for modeling noncooperativehierarchical decision processes, where one player optimizes over a subset of decisionvariables. while taking into account the independent reaction of the other player to his orcourse of action, Bilevel programming is an important area of current research stimulated byits intrinsically very difficult nature and is still :J little known technique, rarely used despite allits potential capabilities. In this note a definition for a general bilevcl programming someapplications, geometric characterization and solution approaches arc presented with someexamples.