International Journal of Computer Applications (0975 – 8887) Volume 113 – No. 11, March 2015 18 Inventory Model for Decaying Items with Multivariate Demand and Variable Holding Cost under the Facility of Trade-Credit Anupam Swami Assistant Professor Govt. P.G. College Sambhal, U.P. Sarla Pareek Professor and HOD Banasthali University Jaipur, RAJ. S.R. Singh, Ph.D. Associate Professor CCS University Meerut, U.P. Ajay Singh Yadav, Ph.D. Assistant Professor SRM University NCR Campus, GZB ABSTRACT In this study, an inventory model for deteriorating items with multivariate demand and variable holding cost is developed. The facility of allowable delay in payment is also taken into consideration. During this period retailer can use the ensued money from sales of the supplied goods to earn interest. Demand rate is a function of on hand inventory and selling price of the item and it is considered that the stock affects the demand rate up to an assured time. Therefore, retailer will order more quantity to stimulate demand rate and to earn more money. Different cases of allowable delay in payment are discussed. The objective of this study is to maximize the retailer’s total profit per unit time. The results are illustrated with some numerical examples and sensitivity analysis for each case is also carried out. Keywords Inventory Model, Sensitivity Analysis, and consumption rate 1. INTRODUCTION The classical inventory models consider the demand rate to be either constant or time-dependent but independent of the available stock status. However, in many practical situations customers’ purchasing manners may be affected by factors such as selling price, on hand inventory and so on. As deliberated by Levin et al. (1972) and Silver and Peterson (1985), sales at the retail point tend to be proportional to inventory displayed and a large piles of goods exhibited in a supermarket will escort the purchasers to buy more. Many marketing researchers and practitioners have paying attention to investigate the modelling aspects of this occurrence. Gupta and Vrat (1986) first designed a model for consumption environment to minimize the cost with the assumption that demand rate is a function of the initial stock level. Mandal and Phaujdar (1989), Datta and Pal (1990), Padmanabhan and Vrat (1995) further developed inventory models under stock- dependent consumption rate with some different assumptions. Since a firm may use a pricing strategy to stimulate demand for its seasonal goods, the inventory problems with selling price and stock dependent demand cannot be disregarded. Urban and Baker (1997) investigated a deterministic inventory problem in with multivariate demand rate. Datta and Paul (2001) analyzed an inventory system where the consumption rate of the goods is affected by both displayed stock level and selling price. You (2005) investigated an inventory model by considering price and time dependent demand rate. Some inspiring research articles associated to this research environment are, You and Hsieh (2007), Chang et al. (2010), Lee and Dye (2012). In today’s business communications, it is more and more frequent to see that the supplier allows the retailer a fixed time (trade-credit) period. This provides an advantage to the retailer, as he/she does not has to pay the supplier immediately after receiving the items; in contrast during the delay period an interest can be earned by the retailer on the accumulated revenue. On the other hand, the strategy of allowing a permissible delay period is also beneficial for the supplier as it attracts new retailers/purchasers who consider this policy to be a type of purchasing cost reduction. Based on this phenomenon, Goyal (1985) analyzed the effect of trade credit on the optimal inventory policy. Later on, Aggarwal and Jaggi (1995) extended Goyal (1985) model with an exponential deterioration rate under the policy of allowable delay in payments. Jamal et al. (1997), Chang and Dye (2001) put forwarded inventory models with trade-credit policy by considering shortages. Teng (2002) proposed an inventory model by estimating the difference between unit selling price and unit cost and recognized an easy analytical closed-form solution to the problem. Sana and Chaudhuri (2008) analyzed optimal trade-credit policies when a price discount is offered. Khanra et al. (2011) proposed an EOQ (Economic Order Quantity) model for a deteriorating item having time dependent demand rate when delay in payment is permitted. Teng et al. (2012) deliberated an inventory model with non- decreasing demand and trade-credit financing. The above mentioned literature reveals that inventory models for decaying items under the condition of allowable delay in payment with variable holding cost, stock and price dependent demand rate, while the on hand inventory affects the demand rate up to a assured period are not discussed so far. Therefore, in this study, an inventory model for deteriorating items with multivariate rate is developed. It is assumed that a trade credit period is offered by the supplier to the retailer. The time dependent holding cost is also taken into consideration. Three cases are discussed according to the situation of the delay period. To validate the concept of this study numerical examples are provided and sensitivity analysis for different cases is also discussed. The concavity of the profit function in each case is disclosed graphically. 2. NOTATIONS AND ASSUMPTIONS The following notation is used throughout the paper: () It The inventory level at any time t , 0 t  T Cycle length (time units) Q The replenishment/order size (units/cycle)