Volume IV, Issue XII, December 2015 IJLTEMAS ISSN 2278 – 2540 www.ijltemas.in Page 1 Inventory Model with Different Deteriorating rates under Exponential Demand, Inflation and Permissible Delay in Payments Raman Patel 1 , D. M. Patel 2 1 Department of Statistics, Veer Narmad South Gujarat University, Surat, INDIA 2 Department of Commerce, Narmada College of Science and Commerce, Bharuch, INDIA Abstract: An inventory model with different deterioration rates under exponential demand with inflation and permissible delay in payments is developed. Holding cost is taken as linear function of time. Shortages are not allowed. Numerical examples are provided to illustrate the model and sensitivity analysis is also carried out for parameters. Key Words: Inventory model, Varying Deterioration, Exponential demand, Time varying holding cost, Inflation, Permissible delay in payments I. INTRODUCTION n recent years much work has been done regarding inventory models for deteriorating items. Ghare and Schrader [6] first developed an EOQ model with constant rate of deterioration. Covert and Philip [5] extended this model by considering variable rate of deterioration. Shah [14] further extended the model by considering shortages. The related work are found in (Nahmias [12], Raffat [13], Goyal and Giri [8]). Goyal [7] first considered the economic order quantity model under the condition of permissible delay in payments. Aggarwal and Jaggi [1] extended Goyal’s [7] model to consider the deteriorating items. The related work are found in (Chung and Dye [4], Chang et al. [3]). Buzacott [2] developed the first economic order quantity model by considering inflationary effects into account. Su et al. [16] developed model under inflation for stock dependent consumption rate and exponential decay. Moon et al. [11] developed models for ameliorating / deteriorating items with time varying demand pattern over a finite planning horizon taking into account the effects of inflation and time value of money. An inventory model for stock dependent consumption and permissible delay in payment under inflationary conditions was developed by Liao et al. [10]. Singh [15] developed an EOQ model with linear demand and permissible delay in payments. The effect of inflation and time value of money were also taken into account. Inventory models for non-instantaneous deteriorating items have been an object of study for a long time. 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 with different deterioration rates for the cycle time and exponential demand under time varying holding cost and permissible delay in payment. Shortages are not allowed. Numerical example is provided to illustrate the model and sensitivity analysis of the optimal solutions for major parameters is also carried out. II. ASSUMPTIONS AND NOTATIONS NOTATIONS: The following notations are used for the development of the model: D(t) : Demand is an exponential function of time t (ae bt , a>0, 0<b<1) A : Replenishment cost per order c : Purchasing cost per unit p : Selling price per unit h(t) : x+yt, Inventory variable holding cost per unit excluding interest charges M : Permissible period of delay in settling the accounts with the supplier T : Length of inventory cycle I e : Interest earned per year I p : Interest paid in stocks per year R : Inflation rate I(t) : Inventory level at any instant of time t, 0 ≤ t ≤ T Q : Order quantity θ : Deterioration rate during μ 1 ≤ t ≤ μ 2 , 0< θ<1 θt : Deterioration rate during , μ 2 ≤ t ≤ T, 0< θ<1 π : Total relevant profit per unit time. ASSUMPTIONS: The following assumptions are considered for the development of the model. I