Optimal integrated production-inventory system for defective items

This article develops a single-manufacturer single-retailer production-inventory model in which the manufacturer's production process is imperfect and it produces a random proportion of defective items in the production period. The manufacturer deliveries ordered items to the retailer with equal-sized shipments policy. The retailer performs a 100% screening process to identify the defective items immediately after receiving the order from manufacturer and handles defective items in multiple batches at the end of each shipment period. The objective is to minimize the expected average total joint annual cost of the integrated production-inventory system with optimal shipment quantity, shipment number and handling number of defective items. Finally, numerical examples are presented to illustrate the application of the proposed model.