This paper presents an extended production inventory model in which the production rate at any instant depends on the demand and the inventory level. The effects of the time value of money are incorporated into the model. The demand rate is a linear function of time for the scheduling period. The proposed model can assist managers in economically controlling production systems under the condition of considering a discounted cash flow. A simple algorithm computing the optimal production-scheduling period is developed. Several particular cases of the model are briefly discussed. Through numerical example, sensitive analyses are carried out to examine the effect of the parameters. Results show that the discount rate parameter and the inventory holding cost have a significant impact on the proposed model.