Inventory is a stock of products. It is kept for future use. We assume that the retailer paid for the items as soon as the items are received. However, in practice the supplier will offer the retailer a delay period. The retailer can sell the goods and accumulate revenue and earn interest. A higher interest is charged if the payment is not settled commodities. An implicit assumption is that the items are obtained from an outside supplier and the entire lot size is deliver at the same time than we are effectively assume that the replenishment rate is infinite. When the replenishment rate is much larger than the demand rate, this assumption is probably satisfactory as an approximation. However, if the rate of replenishment is comparable to the rate of demand, Goyal’s analysis (1985) needs to be modified to reflect this situation. In this paper the main purpose of the study is to extend Goyal’s model (1985) to the case that all items are replenished at a finite rate.