1. Introduction
One of the key assumptions of the basic economic order quantity (EOQ) model is that the items received are of perfect quality. However, product quality is not always perfect but is directly affected by the reliability of the production process used. Therefore, the process may deteriorate and produce defectives or poor quality items. Porteus (1986) introduced a model that shows a significant relationship between quality and lot size. He incorporated the effect of defective items into the basic EOQ model and introduced the option for investing in process quality improvement by means of reducing the probability that the process moves out of control. Lee and Rosenblatt (1987) addressed the problems of joint control of production cycles or manufacturing quantities, and maintenance by inspections. They solved the problem of simultaneous determination of economic manufacturing quantity (EMQ) and the inspection schedule by using an approximation method to the cost function. They also examined the cost penalties of using the classical EMQ and the effects of different parameters of the system on the magnitude of these penalties. Schwaller (1988) extended the EOQ model by adding the assumptions that defective items of a known proportion were present in incoming lots and that fixed and variable inspection costs were incurred in finding and removing these defective items. It was also assumed that the supplier reimbursed the buyer for any defective items found and removed. Cheng (1991)