Economic production quantity (EPQ) model is analyzed for trended demand and the units which are subject to constant rate of deterioration. The system allows rework of imperfect units and preventive maintenance time is random. The proposed methodology, a search method used to study the model, is validated by a numerical example. Sensitivity analysis is carried out to determine the critical model parameters. It is observed that the rate of change of demand and the deterioration rate have a significant impact on the decision variables and the total cost of an inventory system. The model is highly sensitive to the production and demand rate.