A periodic review model for vendor-buyer system with inspection errors and adjusted production rate

The aim of this paper is to develop an integrated single vendor-buyer inventory problem with periodic review policy. The model considers inspection errors, partial backorder, adjusted production rate, dan variable lead time. The buyer faces stochastic demand and uses periodic review model to control the inventory level. An inspection process is established by the buyer to categorize the items received from the vendor. An inspection process is imperfect. The inspector may incorrectly classify the item. Defective items found by the inspector will be returned to the vendor at next delivery. The shortages are allowed in the model and are assumed to be partially backordered. The aim of this model is to determine the optimal review period, optimal number of delivery, and the optimal production rate so that can minimize the total cost supply chain system. Further, a numerical example is given to illustrate the application of the proposed model.