IOSR Journal of Business and Management (IOSR-JBM) e-ISSN: 2278-487X, p-ISSN: 2319-7668. Volume 12, Issue 3 (Jul. - Aug. 2013), PP 37-42 www.iosrjournals.org www.iosrjournals.org 37 | Page Inventory Management Models with Variable Holding Cost and Salvage value R.Mohan 1 , R.Venkateswarlu 2 1 (Mathematics Dept, College of Military Engineering- Pune, India) 2 (GITAM School of International Business -GITAM University, Visakhapatnam, India) Abstract: Inventory management models are developed for deteriorating items when the demand rate is assumed to be linear function of time and the deterioration rate is proportional to time. The model is solved when shortages are allowed. The salvage value is used for deteriorated items in the system. A numerical example is taken to discuss the sensitivity of the models. Key words: Deterioration rate, linear demand, salvage value, shortages, Time-dependent models, I. Introduction The assumption of constant demand rate is not always applicable to many inventory items like electronic goods, vegetables, food stuffs, fashionable clothes etc., since fluctuations in demand rate. Introducing new products will attract more in demand during the growth phase of their life cycle. It is evident that, some product may decline due to the introduction of new products due to the preference or influencing customer’s choice. So it is worth attempt the phenomenon to develop deteriorating inventory models with time-varying demand rate pattern. In developing Inventory models two kinds of time-varying demands so far (i) Continuous time & (ii) discrete time. Many continuous –time inventory models have been developed taking in to the consideration like linearly increasing /decreasing demand [i.e., D(t) = a + bt ] 0 0 , 0 [    b or b a . Ghare and Schrader (1963) studied an inventory model for exponentially decaying. Covert and Philip (1973) developed an inventory model for time dependent rate of deterioration. Aggarwal (1978) proposed an order level inventory model for a system with constant rate of deterioration. Dave and Patel (1981) studied a lot size model for time proportional demand with constant deterioration. Deb and Choudhuri (1987) studied a heuristic approach for replenishment of trended inventories with shortages. Hariga (1995) developed an inventory model of deteriorating items for time-varying demand with shortages. Chakraborti and Choudhuri (1996) proposed an EOQ model for deteriorating items of linear trend in demand with shortages in all cycles. Giri and Chaudhuri (1997) developed a heuristic model for deteriorating items of time varying demand and costs considering shortages. Goyal and Giri (2001) studied survey of recent trend in deteriorating inventory model. Mondal et. al (2003) developed an inventory model of ameliorating items for price dependent demand rate. You (2005) studied the inventory system for the products with price and time dependent demands. Ajanta Roy (2008) proposed an inventory model for deteriorating items with price dependent demand and time varying holding cost with and without shortages. Mishra and Singh (2010) studied an inventory model for deteriorating items with time dependent demand and partial backlogging. Recently, Mishra (2012) developed an inventory model with Weibull rate of deterioration and constant demand. He incorporated variable holding cost considering shortages and also salvage value. Vikas Sharma and Rekha (2013) developed an inventory model for time dependant demand for deteriorating items with Weibull rate of deterioration and shortages. In this paper, we consider an order level inventory problem with time-dependent deterioration when the demand rate is a linear function of time. Shortages are allowed in this case and the time horizon is infinite. The optimal total cost is obtained considering the salvage value for deteriorated items. The sensitivity analysis is done with numerical example. II. Assumptions and notations The mathematical model is developed on the following assumptions and notations: (i) The demand rate D(t) at time t is assumed to be D(t) = a+bt, , 0 , 0   b a . (ii) Replenishment rate is infinite and lead time is zero. (iii) A, the ordering cost per order is known and constant. (iv) θ(t) = θt is the deterioration rate, 0 < θ < 1. (v) C, the cost per unit (vi) h+αt, h>0, α>0, the holding cost per unit (vii) I(t) is the inventory level at time t. (viii) The order quantity in one cycle is q.