Bilevel Programming Problems In Management Decision

Management decision problem exists in all aspects of human social life, because of the complexity of the problems and shortcomings in the current theoretical study, only local interests, while ignoring the overall interests, is currently the management decision-making in the presence of a more general problem. Bilevel programming characteristics exactly considering the decision making system hierarchy, from an overall perspective, considering the global, hope to achieve global optimal. Therefore, in the management decision problems in application of bilevel programming theory and method, will get better effect.With the development of world economic integration and market globalization, supply chain management has become an important management model of modern enterprises, the competition between enterprises is no longer a simple individual competition, but the competition between chain and chain. Each member in the chain is independent interests of enterprises, their interests are organized together; from the final consumer upstream suppliers to the downstream, each member enterprise can be abstracted as a node, node between the buyer seller relationship together, forming a hierarchical decision structure. The paper carried out a detailed analysis on the process of the supply chain upstream and downstream enterprises decision, discusses bilevel programming model to describe the supply chain strategic partnership between the possibility of logistics planning, constructs a set of the supply chain upstream and downstream enterprises overall profit, total logistics costs a minimum of bilevel programming model.Bilevel programming problem is essentially non convex, non differentiable and non constraint region connectivity which bring a great deal of difficulties to the numerical solution, especially to obtain the global optimal solution in the feasible algorithm is not much, the existing research results are very few. In this paper, based on reverse convex constrained optimization technique, a new parallel cutting plane algorithm is proposed for bilevel linear programming. This algorithm not only can obtain the global optimal solution, and small workload, overcome the non convex, constrained region of non connectivity, from outside of the feasible region gradually approaching the global optimal solution for bilevel linear programming.Hierarchical decision in the actual context, decision objective of upper and lower level decision makers are often nonlinear, and the allowable variation range of decision variables is decided by the objective conditions, the function expression may be nonlinear. For bilevel nonlinear programming(BNLP), there is not much effective algorithm and application. In this paper, a special class of bilevel nonlinear programming, which has linear objective function and nonlinear constraint function, is discussed. BNLP is transformed into an optimization problem with a reverse convex constraint, the geometric properties of solution is discussed, a new algorithm to find the global optimal solution is established, and the convergence of the algorithm is proved.Finally, the paper summarizes the work, and the future works are discussed.