Analysis of Supply Chain Coordination under Uncertain Demand Quantity Discount Contract

Considering a single two-stage supply chain, which is consisting of a supplier and a retailer, market demand is uncertain, before the beginning of sales activities, supplier and retailer need to determine their optimal stratege. The paper respectively analysis the Nash equilibrium of the four cases: certain and uncertain market demand, with and without quantity price discount contract. Because the Nash equilibrium of the uncertain demand quantity price discount contract is closely related to the market demand distribution function, so use the uniform distribution as an example, solves the supplier's optimal quantity price discount contract and retailer's optimal quantity, analysis the change trend of the supplier's optimal discount rate and the retailer's optimal order quantity with the related parameters change, and analysis the size of the profit's mathematical expectation. The research results show that when demand is uncertain, the quantity price discount contract can increase the expected profits, make both the supply and demand sides to achieve the "win-win" cooperation, realize supply chain coordination.