Design of optimal quantity discounts for multi-period bilevel production planning under uncertain demands

The analysis of the quantity discount of the decentralized supply chain has been studied only for single-period planning models. This article presents the design of an optimal quantity discounts for multi-period bilevel production planning for two-echelon supply chains under demand uncertainty. In order to derive an optimal contract for multi-period production planning, the cumulative order quantity and production quantity are introduced. From our proposed model, a Stackelberg equilibrium is analytically derived for the supply chain when the supplier is the leader and the retailer is the follower. An optimal discount contract is analytically designed through the optimal solution of the centralized problem. Computational results show the effectiveness of the proposed discount contract under demand uncertainty.