Optimal input quantity decisions considering commitment order contracts under yield uncertainty

We examine a two-echelon supply chain with one supplier and one retailer under yield and demand uncertainty. A basic model is developed, in which the supply chain is assumed to operate under Vendor-Managed Inventory (VMI). Commitment order contracts are then proposed, and three possible situations are investigated: (1) The wholesale price of the commitment order equals the wholesale price of the regular order; (2) the wholesale price of the commitment order is-lower than-the wholesale price of the regular order; (3) the wholesale price of the commitment order is higher than the wholesale price of the regular order. Given the retailer's commitment order quantities, we obtain the supplies optimal input quantities under different conditions. The impact of the retailer's commitment order quantity on the supplier's input quantity decision is also examined. Furthermore, the retailer's optimal commitment order quantities are discussed. We demonstrate the detailed boundary conditions for all possible optimal solutions of both members. Our analysis reveals that commitment order contracts are effective to stimulate the input quantity of the supplier. However, there still exist several regions in which the supplier's input quantity is independent of the commitment order quantity. In the special situation, we find that the supplier's input quantity decreases with the commitment order quantity. The numerical example shows that, with special sets of wholesale prices, the commitment order contracts can be used to improve the performance of the supply chain facing different random yield environments.