Optimization and coordination of supply chain with revenue sharing contracts and service requirement under supply and demand uncertainty

In a one-supplier-one-buyer supply chain, uncertainty occurs not only at the demand side, but also at the supply side, which is commonly observed in business. Optimization and coordination of such a supply chain is rarely investigated in literature, especially with service requirement. In this paper we model the supply chain with revenue sharing contract and service requirement under supply and demand uncertainty. Firstly, we derive the buyer's and the supplier's optimal policies, and find the conditions to coordinate the supply chain. Secondly, we prove that the buyer's and the supplier's optimal quantities are both non-decreasing of the service requirement. We also find there exists an optimal supply quantity for the supplier, if the buyer's ordering quantity based on her service requirement exceeds the supplier's optimal supply quantity, then the supplier's profit is a non-increasing function of the buyer's order quantity; otherwise, the supplier's profit is a non-decreasing function of the buyer's order quantity. Thirdly, by comparing with the benchmark supply chain model where only demand uncertainty is considered, we find that in the coordinated supply chain under supply and demand uncertainty, the revenue sharing ratio for the supplier will be higher if the wholesale price remains the same, or the wholesale price will be higher if the revenue sharing ratio for the supplier keeps the same.