Fuzzy linear bilevel optimization: Solution concepts, approaches and applications

Abstract

Bilevel programming provides a means of supporting two level non-cooperative decision-making. When a decision maker at the upper level (the leader) attempts to optimize an objective, the decision maker at the lower level (the follower) tries to find an optimized strategy according to each of the possible decisions made by the leader. A bilevel decision model is normally based on experts' understanding of possible choices made by decision makers at both levels. The parameters, either in the objective functions or constraints of the leader or the follower in a bilevel decision model, are therefore hard to characterize by precise values. Hence this study proposes a fuzzy parameter linear bilevel programming model and its solution concept. It then develops three approaches to solve the proposed fuzzy linear bilevel programming problems by applying fuzzy set techniques. Finally, a numerical example and a case study illustrate the applications of the proposed three approaches. © 2007 Springer-Verlag Berlin Heidelberg.