In the classical inventory models, it is assumed that the demand for production items is continue, however, there are various types of manufactured products that demand for their items is discrete and periodic. In this paper, an inventory control model for production systems is developed with discrete demand and interval time between two sequential demands is same. Also, assumed the demand is dependent to the price which demand decreases linearly with the increase in price. We suggest a mixed integer mathematical model and the purpose of this model is maximizing the profit by determining the optimal selling price and replenishment quantity. Mathematical theorems are developed to determine the optimal selling price and replenishment quantity for continue decision variable and then we purposed an algorithm for finding optimal discrete value for the number of periods of demand at the production time and optimal price selling. A numerical example is given to illustrate the theory.
