A solution to interval linear bi-level programming and its application in decentralized supply chain planning

Decentralized supply chain planning problems naturally combine multiple decision steps, which are connected in a hierarchical way. Different participants usually have incomplete information for various reasons, such as ego-defense. In this paper, the linear bi-level programming with interval coefficients in lower level objective function is formulated as an extension of the classical linear bi-level problem under an inexact environment. The best solution, best value and best coefficients are defined, respectively. Moreover, a method based on Kth-best algorithm is employed to solve the problem; the coefficients´ impact on solution is analyzed, and a numerical example is presented to illustrate effectiveness of the present method. Finally, advantages of the method in decentralized supply chain planning are discussed.