A finite production model with random defective rate and shortages allowed and backordered

This paper examines the problem of random defective rate on the economic production quantity (EPQ) model with backlog permitted. One of the unrealistic assumptions of classic finite production model is that it assumes manufacturing facility functions perfectly at all times. However, in most practical settings, due to process deterioration or other factors, defective items are generated. In this paper, a random defective rate is considered and all defective items are assumed not repairable. Because of the random scrap rate, it follows that the cycle length of production is not a constant. The renewal reward theorem is employed to deal with the variable cycle length. Disposal cost per scrap item is included in cost analysis, an optimal production quantity that minimizes the expected overall costs for the imperfect quality EPQ model is derived, where backlog is permitted.