International Journal of Latest Technology in Engineering, Management & Applied Science (IJLTEMAS) Volume VI, Issue VIIIS, August 2017 | ISSN 2278-2540 www.ijltemas.in Page 1 Inventory Model with Different Deterioration Rates for Imperfect Quality Items and Inflation considering Price and Time Dependent Demand under Permissible Delay in Payments Shital S. Patel Department of Statistics, Veer Narmad South Gujarat University, Surat, INDIA Abstract: One of the assumptions for an economic order quantity model is that all items received in an order are of perfect quality is not always fulfilled. Some of the items are of defective quality in the lot received. Another assumption is that as soon as items are received, payments are made. In today’s competitive the supplier allows certain fixed period known as permissible delay for payment to the retailer for settling the amount of items received. Keeping this reality, a deterministic inventory model with imperfect quality is developed when deterioration rate is different during a cycle. Here it is assumed that demand is a function of time and price. Numerical example is taken to support the model. Sensitivity analysis is also carried out for parameters. Key Words: Inventory model, Varying Deterioration, Time dependent demand, Price dependent demand, Defective items, Inflation, Permissible Delay I. INTRODUCT ION ost of the items lose their characteristics overtime and this characteristic is defined as deterioration. Ghare and Schrader [8] considered inventory model with constant rate of deterioration. Covert and Philip [7] extended the model by considering variable rate of deterioration. Mandal and Phaujdar [14] presented an inventory model for stock dependent consumption rate. Haiping and Wang [11] studied an economic policy model for deteriorating items with time proportional demand. Patel and Parekh [17] developed an inventory model with stock dependent demand under shortages and variable selling price. Other research work related to deteriorating items can be found in, for instance (Raafat [20], Goyal and Giri [10], Ruxian et al. [22]). In reality, it happens that units ordered are not of 100% good quality. Rosenblat and Lee [21] were the first to focus on defective items. Salman and Jaber [24] developed an inventory model in which items received are of defective quality and after 100% screening, imperfect items are withdrawn from the inventory and sold at a discounted price. Salman and Jaber’s [24] model was extended by Wee et al. [26] by allowing shortages. Chang [4] studied an inventory model to investigate the effects of imperfect products on the total inventory cost associated with an EPQ model. Patel and Patel [18] developed an EOQ model for deteriorating items with imperfect quantity items. Hauck and Voros [12] considered inventory model in which percentage of defective items as a random variable and defined the speed of the quality checking as a variable. An economic order quantity model under the condition of permissible delay in payments was developed by Goyal [λ]. Aggarwal and Jaggi [1] extended Goyal’s [λ] model to consider the deteriorating items. The related work are found in (Chung and Dye [5], Salameh et al. [23], Chung et al. [6], Chang et al. [3]). The effect of inflation and time value of money play important role in practical situations. Buzacott [2] and Mishra [15] simultaneously developed inventory model with constant demand and single inflation rate for all associated costs. Mishra [16] considered different inflation rate for different costs associated with inventory model with constant rate of demand. An inventory model for stock dependent consumption and permissible delay in payment under inflationary conditions was developed by Liao et al. [13]. An EOQ model with linear demand and permissible delay in payments was considered by Singh [25]. The effect of inflation and time value of money were also taken into account. An inventory model with inflation and permissible delay in payments was considered by Patel and Patel [19]. Generally the products are such that there is no deterioration initially. After certain time deterioration starts and again after certain time the rate of deterioration increases with time. Here we have used such a concept and developed the deteriorating items inventory models. In this paper we have developed an inventory model for imperfect quality items with different deterioration rates. Demand of the product is time and price dependent for the cycle under time varying holding cost. Shortages are not allowed. To illustrate the model, numerical example is M