An economic order quantity with imperfect quality and quantity discounts

Previous studies in the issue of inventory models with imperfect quality assumed the defectives could be sold in a batch by the end of the inspection process and the manufacturing systems were push systems. However, the above assumptions may not be true in the pull system in which buyer is powerful. Therefore, in this paper, we develop a new inventory model for items with imperfect quality and quantity discounts where buyer has exerted power over its supplier. Based on the concept of powerful buyer, there are three considerations included in this new model: (1) the order quantity is manufactured at one setup and is shipped over multiple deliveries, (2) the defectives are screened out by a 100% inspection for each shipment but sold in a batch by the end of inspection at the last shipment of each cycle, and (3) the supplier offers quantity discounts to response the request of the powerful buyer. Further, an algorithm is developed to help the powerful buyer to determine the optimal order policy accurately and quickly. Two numerical examples are available in this paper to illustrate the proposed model and algorithm. Besides, based on the numerical examples, a sensitivity analysis is made to investigate the effects of four important parameters (the inspection rate, the defective rate, the receiving cost, and the ordering cost) on the optimal solution.