For certain types of inventory, the ordering cycle and demand may be random variants, which satisfy certain types distribution. The classical EOQ model usually neglects the fact. Based on the constant demand, under the hypothesis that the ordering cycle is a random variant which satisfies exponent distribution, average demand is a linear increasing function, this paper considers the effects of the time-value of capital and inflation on replenishment strategy of inventory system. Loosening the condition of basic economic order quantity model under deterministic state, the total cost function of the model is provided. The optimum order quantity and cycle are obtained. The application range of EOQ model under the constant demand is widened. The theoretical evidence is provided for the inventory system to make management decision.