In this paper, the inventory models assumed that the production rate of a manufacturing system is often assumed to be constant, but in fact production rate is a variable under managerial control. Production rate may be influenced due to demand, on hand inventory and launching new competitive product or with the change in customer’s preferences. A great number of authors have studied problems connected with constant production rate by taking different deterioration and demand rate. But when a new product is launched in the super market, demand increases more rapidly as time progresses.