Optimal inventory model in which the imperfect items will be repaired after the screening process

The aim of this paper is defining an optimal model for a retailer who uses a 100% screening process to reveal defective items which are received from the supplier. The demand rate is lower than the screening rate and the defective items will be sent to a repairing shop to be repaired. According to the fixing rate, the products will be sent back to the retailer after a while. During the fixing process the retailer may face shortages. The goal is finding the ordering amount to maximize the retailer's profit during the planning horizon. The mathematical model will be described and renewal-reward theorem will be used to solve the proposed model considering a numerical example