An EOQ model of inventory for items with linear rate of deterioration is considered, taking the demand rate to be dependent on the stocjk level at any instant of time. The Payments are permitted to be delayed up to certain period of time. Shortages are not allowed. After the certain period, a special discount is permitted to reduce the stock in inventory because if the stock is holded, an interest is paid at a pre-decided rate depending on the items on hand. To avoid the interest payment, we introduce the discount to clear the items in stock.