Optimization of Multi-Period Bilevel Supply Chain Planning for Single Supplier and Single Retailer under Demand Uncertainty

Abstract

This paper presents the optimization of multi-period bilevel supply chain planning for single supplier and single retailer with leader-follower relationship under demand uncertainty. The multi-period production planning problem for the supplier and the retailer is formulated as the mixed integer nonlinear bilevel programming problem. In order to improve the total profit, the effects of the replacement of leader-follower relationship are investigated. The effectiveness of the replacement of leader-follower relationship is examined by some numerical experiments. A quantity discount contract with quadratic function is also proposed to maximize the total profit under demand uncertainty .