AN INVENTORY MODEL FOR DETERIORATING ITEMS WITH ON HAND INVENTORY DEPENDENT RAMPED TYPE DEMAND RATE D. Samal 1 , A. Kalam 2 , S.K.Sahu 3 & M. Mishra 4 This model discuss an infinite time horizon deterministic inventory model for deteriorating items without shortages where the demand rate declines along with stock level down to a certain level of inventory and also the demand rate becomes constant for the rest of the cycle and the deterioration is a ramp type function. The decision rule for finding the optimal order quantity is also given. Five numerical examples are presented to illustrate the model developed. Keywords: Inventory, Shortage, Demand, Deterioration, Ramp. INTRODUCTION The classical inventory models consider the demand rate to be either constant or to be time dependent but independent of the stock status. However for certain types of inventory, particularly consumer goods, and the consumption rate may be influenced by the stock levels, that is, the consumption rate may go up or down with the on-hand stock level. As reported by Levin et al [1972] and Silver and Peterson [1985], sales at the retail level tend to be proportional to inventory displayed and a large piles of goods displayed in a supermarket will lead the customers to bye more. These observations have attracted many marketing researchers and practioners to investigate the modeling aspects of this phenomenon. Gupta and Vrat [1986] first developed a model for consumption environment to minimize the cost with the assumption that stock- dependent consumption rate is a function of the initial stock level. Silver and Meal [1973], Datta and Pal [1988] has progressed the model where demand rate is not required to be constant. Among the important paper published so far with inventory-level-dependent demand rate, mention may be made of by Gupta and Vrat [1986], Mandal and Phaujdar [1989], baker and Urban [1988] etc. Gupta and Vrat[1986] have discussd a situation where the demand rate has been assumed to dependent on the order quantity whereas, Mandal and Phaujdar[1989] have discussed an inventory level. Baker and Urban[1988] have analyzed a similar situation assuming the demand rate to be dependent on the 1 Department of Mathematics, College of Engineering Bhubaneswar, Orissa 2 Department of Mathematics, MIT, Taraboi, Khurda-752055, Orissa 3 Department of Mathematics, Govt Science College Malkanagiri, Orissa 4 NIFM, Sector-48, Pali Road Faridabad-121001, Haryana Email: abdul_003m@rediffmail.com on-hand inventory according to the relation () Ri i β =α where 0, 0 1 α> <β< . Sahu et al have analysed a similar situation, assuming the demand rate to be depend on the on-hand inventory i according to the relation () i Ri e -β =α where 0, 0 1 α> <β< . The present inventory model makes an attempt to study the situation where the demand rate decline along with stock level down to a certain level of inventory and also the demand rate become constant for the rest of the cycle. It is well known that the stock level has a motivation affect on the customers but the experience shows that customers arrive to purchase goods attracted by huge stockdown to a certain level of declining inventory. The only a limit numbers of customer arrive to purchase goods owing to such factors goodwill, good quantity, genuine price level of the goods, locality of the shop, good quality of the items etc. The present model is applicable in such a situation when the β approaches to zero. FUNDAMENTAL ASSUMPTIONS AND NOTATIONS OF THE MODEL The basic assumption made to develop the proposed model are the following: 1. Replenishment rate is infinite i.e, replenishment is instantaneous but replenishment size is finite. 2. Lead time is zero. 3. No shortages are permitted. 4. The selling price s, unit cost C, holding cost C 1 per unit per unit time and replenishment cost C 3 per replenishment are known and constant. 5. The time horizon is finite. 6. The inventory system involves only one item. 7. The demand rate is dependent on the on-hand inventory down to a level S 0 , beyond which it is International Journal of Information Technology and Knowledge Management July-December 2010, Volume 2, No. 2, pp. 519-521