We study an inventory system with linear time varying exponential distributed deterioration in which production and demand rates are constant. The mathematical model is developed to obtain the total cost per unit time of an inventory system. The inventory controlling systems in terms of first order differential equations are solved numerically. The optimal cycle time is derived and the results are applied to numerical problems. The effect of changes in the model parameters on decision variables and the average total cost of an inventory system are studied through numerical examples.
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