International Journal of Engineering Research ISSN: 2348-4039 & Management Technology July-2017 Volume 4, Issue-4 Email: editor@ijermt.org www.ijermt.org Copyright@ijermt.org Page 93 STUDY OF AN INVENTORY MODEL FOR DECAYING ITEMS WITH STOCK DEPENDENT DEMAND AND EXPONENTIAL PRODUCTION RATE SANDEEP KUMAR IIMT University Meerut ABSTRACT In the present paper a volume flexible manufacturing system is considered for a decaying item with an inventory-level-dependent demand rate. In reality, the demand rate remains stock-dependent for some time and then becomes a constant after the stock falls down to a certain level. Many factors like limited number of potential customers and their goodwill, price and quality of the goods, locality of shop, etc. can be accounted for the change in the demand pattern. INTRODUCTION Inventory is a part of every fact of business life. Without inventory any business can not be performed, whether it being service organization. Under increased competition, inventory based business are forced to better co-ordinate their procurement and marketing decisions to avoid carrying excessive stock when sales are low or shortages when demand are high. An effective means of such co-ordination is to conduct the inventory control and manufacturing decision jointly. The main task is to determine the optimal rate of production and inventory policy for a given time varying demand. In the Classical Economic Production Lot Size(EPLS) model, the production rate of a machine is regarded to be pre-determinded and inflexible1.Alder and Nanda (1974), Sule (1981), Axsater and Elmaghraby (1981), Muth and Spearmann (1983) extended the EPLS model to situations where learning effects would induce an increase in the production rate. Proteus (1986), Rosenblat and Lee (1986) and Cheng (1991) considered the EPLS model in an imperfect production process in which the demand would exceed the supply. Schweitzer and Seidmann (1991) adopted, for the first time, the concept of flexibility in the machine production rate and discussed optimization of processing rates for a FMS (flexible manufacturing system). Obviously, the machine production rate is a decision variable in the case of a FMS and then the unit production cost becomes a function of the production rate. Khouja and Mehrez (1994) and Khouja (1995) extended the EPLS model to an imperfect production process with a flexible production rate. Silver (1990), Moon, Gallego and Simchi-Levi (1991) discussed the effects of slowing down production in the context of a manufacturing equipment of a family of items, assuming a common cycle for all the items. Gallego (1993) extended this model by removing the stipulation of a common cycle for all the items. But the above studies did not consider the demand rate to be variable. It is a common belief that large piles of goods displayed in a supermarket lead the customers to buy more. Silver and Peterson (1985) and Silver (1979) have also noted that sales at the retail level tend to be proportional to the inventory displayed. Baker and Urban (1988) and Urban (1992) considered an inventory system in which the demand rate of the product is a function of the on-hand inventory. Goh (1994) discussed the model of Baker and Urban18 relaxing the assumption of a constant holding cost. Mandal and Phaujder (1989) then extended this model to the case of deteriorating items with a constant production rate. Datta and Pal (1990) presented an inventory model in which the demand rate of an item is dependent on the on-hand inventory level until a given inventory level is achieved, after which the demand rate becomes constant. Giri , Pal , Goswami and Chaudhuri (1995) extended the model of Urban (1992) to the case of items deteriorating overtime. Ray and Chaudhuri (1997) discussed an EOQ (economic order quantity) model with stock-dependent demand, shortage, inflation and time discounting of different costs and prices associated with the system. Ray, Goswami and Chaudhuri (26 studied the inventory problem with a stock-dependent demand rate and two levels of storage, rented warehouse (RW) and own warehouse (OW). Giri and Chaudhuri (1998) extended the model of Goh (1994)