In this paper, we will be considering a case of the subject of imperfection or deficiency in the inventory process of a single commodity which has many components. For example, the deterioration of items in the stock is one component; another component is the quality of the items received in an inventory order. This has been investigated by many like Yano and Lee (1995) and silver (1976) , where the imperfection of the order was due to defectiveness of items and shortages on the supply side

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... the amount of imperfection as a discrete random variable. We shall consider only the case of shortages of supply, but allow for continuous random variables by taking the proportion of shortages relative to the order quantity. A mathematical model is developed where an analytic expression for the economic order quantity is obtained. Special cases for the distribution of the proportion will be presented, along with numerical examples and comparisons to the classical model without shortages. These models considered the imperfection in the ordered lot a discrete random variable with either a Poisson or Binomial distribution. Jaggi and Mittal (2010) investigated the effect of deterioration on the retailer's economic order quantity when the items are of imperfect quality. They assumed the screening rate to be more than the demand rate. This enabled the retailer to fulfill the demand out of the perfect quality products along with the screening process. They found that in the case of highly deteriorating products the retailer should order more frequently to reduce his loss due to deterioration. When the defective items increase and profits decrease, the retailer needs to take corrective www.ccsenet.org/ijbm