An Optimization Approach to Bi-level Quadratic Programming Problems

ABSTRACT. Bi-level programming problems are an important type of multi-variable and double-layer programming problems. These problems appear everywhere especially in the industrial, supply-chain, and marketing programming applications. In this work, two new original approaches are proposed to solve bi-level quadratic programming problems in different cases: the so-called ergodic branch-and-bound method and the iteration method, respectively to solve small and large variable-space problems. These proposed methods show better accuracy and computing efficiency than traditional approaches even when tackling the non-linear (quadratic) bi-level problems which the conventional methods can not solve sometimes. Furthermore, a typical industrial engineering application was introduced as an example to present our new proposed algorithm. In this application, we considered an industrial manufacture-sale network problem with single plant and multiple distribution-sale sites. Using our proposed iteration algorithm, issues such as setting the addresses for sale-sites, fixing the prices and optimal carrying quantity for each of clients are studied at the sale-sites. The application results indicated that the proposed model can be more effectively applicable to realize the maximum benefits for both the sides in the whole network.