Coordinating a vendor–buyer supply chain with stochastic demand and uncertain yield

The paper develops a single-vendor single-buyer supply chain model with stochastic demand and uncertain yield where the vendor delivers the buyer’s order quantity in a number of shipments. We formulate the model considering instantaneous/non-instantaneous supplies from the vendor to the buyer and that the buyer’s replenishment time interval does/doesn’t depend upon the input. The optimal shipment policy is determined by maximizing the average expected profit of the whole supply chain. The model is further extended to consider a revenue sharing contract to align incentives of decentralized partners within the supply chain. Numerical examples are provided to illustrate the developed models. It is observed from the numerical study that the coordinated (integrated) policy is beneficial in comparison to the individual policies made by the supply chain partners.