In this paper, we consider an inventory system in case the toleration to be inventory stortage under the price discount. It has been observed that suppliers suggest a free addition of marketing policy like a price discount. A major reason for a supplier to offering a free addition to a customers is to stimulate the demand and to decrease a total cost. but, If we not adapting to the toleration to be inventory-lacking, we will a burden holding costs in a relation to the holding of inventory. This paper, is a combination of the toleration of inventory shortage and the condition of discount price. The costs are defined as the sum of the ordering, holding, shortage, purchasing and opportunity costs. Based on numerical results, conclusions follow about the total of operation costs the division of the shortage rate of inventory.