A vendor-buyer supply chain model with an imperfect production system and standby key modules

An integrated vendor-buyer supply chain production-inventory model with a vendor and a buyer is considered in the paper. The buyer adopts a continuous review and fixed order lot size policy to deal with a product with stochastic demands. We assume that unmet demands are backordered. A vendor produces and supplies the product to the buyer. A lot-for-lot replenishment policy is implemented between the two parties. When the buyer's reorder point is reached, an order will be placed, and a production run will be started at the vendor when the order is received. The vendor's production system is not perfect during a production run and is affected by a key module. The production system may shift from an in-control state to an out-out-control state when the key module has deteriorated. As a result, defective items may be produced. The vendor can keep standbys of the key module to improve the production system reliability. An iterative solution procedure is developed to obtain a near-optimal solution for the optimal number of standby key modules for the vendor, and the order quantity and the reorder point for the buyer.