The main purpose of this paper is to estimate economic order quantity (EOQ) value within items with two types of imperfect quality under random inspection. The imperfect items are distinguished as defective and reworkable ones. The defective items are treated as scrap and reworkable ones will be sent back to supplier to get repaired. The repaired items later are able to meet customer demand. A mathematical model is developed in which defective and reworkable rate is given under uniform distribution. We consider every probability density function of each good, defective and reworkable proportion following multivariate hypergeometric distribution. Then we extend the study to shortage case that may occur due to the lack of good items to fulfill demand rate during an order cycle. For every shortage, it is assumed that manufacturer has to pay additional penalty cost. The expected total cost is then calculated over its corresponding probability. Interestingly we observed a pattern of the expected total cost value that will drop as number of order quantity increases to a certain point and turn over to increase gradually as number of order increases within a range of order quantity. At last, numerical computation is provided to illustrate the conclusive outcome of proposed model.
Keywords: EOQ, ETCPUT, Shortage, Order Size, Screening Rate, Rework Rate

The main purpose of this paper is to estimate economic order quantity (EOQ) value within items with two types of imperfect quality under random inspection. The imperfect items are distinguished as defective and reworkable ones. The defective items are treated as scrap and reworkable ones will be sent back to supplier to get repaired. The repaired items later are able to meet customer demand. A mathematical model is developed in which defective and reworkable rate is given under uniform distribution. We consider every probability density function of each good, defective and reworkable proportion following multivariate hypergeometric distribution. Then we extend the study to shortage case that may occur due to the lack of good items to fulfill demand rate during an order cycle. For every shortage, it is assumed that manufacturer has to pay additional penalty cost. The expected total cost is then calculated over its corresponding probability. Interestingly we observed a pattern of the expected total cost value that will drop as number of order quantity increases to a certain point and turn over to increase gradually as number of order increases within a range of order quantity. At last, numerical computation is provided to illustrate the conclusive outcome of proposed model.
Keywords: EOQ, ETCPUT, Shortage, Order Size, Screening Rate, Rework Rate

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