Coordinated between single-vendor and single-buyer inventory model with lead time reduction and price discount

This study is to construct an inventory system model in which a single vendor supplies a product to a single buyer. The buyer uses the (R,Q) inventory policy. The inventory model analyzed the problem that the ordering cost reductions depend on lead time in the continuous inspection inventory model with backorders discount. The demand during lead time is distributed as normally distribution. Also, vendor manages the complete items. Then, the minimization of the average total related cost by simultaneously optimizing the order quantity, lead time and backorder price discount is considered. Moreover, a numerical example shows that how the integrated inventory models can be applied to the system. The results indicate that the percentage of average total cost savings depends on the shortened lead time.