Retailer's Ordering Policy in a Supply Chain when Demand is Price and Credit Period Dependent

Trade credit is a well established promotional tool in the present competitive world and its impact on demand cannot be ignored. Businesses often use trade credit to increase their market share and, in turn, the profit. Undoubtedly, trade credit plays a great role in increasing the demand but it also involves a great risk of nonpayment. In order to reduce the risk of non-payment, businessman at times use a partial trade credit policy in which they demand a certain percentage of the total amount from the customer at the time of purchase and offers the credit for the remaining amount. Furthermore, it is also observed that the demand of FMCG is highly price sensitive. In order to see the effect of credit and price together, on demand, the retailer’s demand is taken as a function of price and credit period. Moreover it is assumed that the supplier offers the full credit to the retailer but the retailer passes a partial credit to customers. The inventory model, determines the optimal replenishment time, credit period, and price for the retailer that maximizes profit. Numerical examples have been provided to support the model followed by the comprehensive sensitivity analysis. gains capital, materials and services without any payment during the credit period. Hence both the retailer and the supplier can take advantage of the trade credit policy. As evidence by previous literature including Peterson and Rajan (1997), Nilsen (2002), Fisman and Love (2003), Love et al. (2007), and Ge and Qiu (2007) trade credit is important source of finance for the retailers. The impact of trade credit policy on EOQ was first developed by Goyal (1985). Aggarwal and Jaggi (1995) generalized Goyal’s (1985) model DOI: 10.4018/jsds.2011100104 62 International Journal of Strategic Decision Sciences, 2(4), 61-74, October-December 2011 Copyright © 2011, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited. by extending it for exponentially deteriorating items. More related work can be found in Shinn (1997), Chung (1998), Sarker et al. (2000), Arcelus (2001), Teng (2002), Salameh et al. (2003), Teng et al. (2006), Song and Cai (2006), Jaber (2007), and Sana and Chaudhuri (2008). In all the mentioned models it was assumed that the supplier would offer the trade credit to the retailer but the retailer does not extend this same to his customers. This is termed as one level of trade credit. But, in most business transactions, this assumption is unrealistic. As it is observed that sometimes the retailer tend to also extend this benefit to his customers by offering a delayed payment period, known as two level trade credit. Huang (2003) and Biskup et al. (2003) developed the retailer’s optimal ordering policy under a two-level trade credit policy in which the retailer receives a favorable delayed payment period from the supplier and subsequently provides a delayed payment period to customers. Later, Huang (2006) modified Huang (2003) to incorporate a retailer’s storage space limitation into the model. Huang (2007) extended Huang (2003) to an economic production quantity (EPQ) model with two-level trade credit. In all of the abovementioned articles, it is assumed that the trade credit period offered by the supplier is longer than the trade credit period offered by the retailer. Teng and Goyal (2007) released this assumption and established an EOQ model with two-level trade credit. Chung and Huang (2007) continued to amend Huang (2006) to propose an EOQ model for deteriorating items under the two-level trade credit policy. Liao (2008) developed an EOQ model for exponentially deteriorating items under the two-level trade credit policy. In contrast, Teng and Chang (2009) modified Huang (2007) and developed an EPQ model. Jaggi et al. (2008) developed an EOQ model under a two-level trade credit policy with credit-linked demand. Thangam (2009) extends Jaggi (2008) model for perishable items when demand depends on both selling price and credit period. To reduce default risks, in practice, a retailer sometimes, offers a partial trade credit to its customers who must pay a portion of the purchase amount at the time of placing an order as a collateral deposit, and then gets a credit on the rest of the outstanding amount. Huang (2005) developed an optimal retailer’s policy for one level where the supplier offers partial credit to the retailer. Adding to this, Huang and Hsu (2008) proposed an EOQ model with a two-level trade credit policy in which the retailer obtained the full trade credit from the supplier, but only offered a partial trade credit to end customers. However he has ignored the fact that the retailer offers his customer a permissible delay period N hence the retailer receives his revenue till T+N and not till N. Recently, Teng (2009) developed an optimal ordering policies for a retailer who offers distinct trade credits to its good and bad credit customers. But, in his paper he has considered demand to be constant whereas, in real practice it has been observed that the demand does get influenced with the credit period and the price. Here, in this paper we extend Teng (2009) for price as well as credit sensitive demand. Numerical example is presented to illustrate the theoretical result followed by some managerial applications. ASSUMPTIONS AND NOTATIONS The assumptions and notations throughout this study are as follows: 1. The discussion and analysis in this paper is restricted to the case of a single-supplier, single-retailer and many customers of a specific product. 2. Demand is credit as well as selling price dependent. 3. Shortages are not allowed. 4. Time horizon is infinite. 5. Replenishments are instantaneous. 6. The retailer gets full trade credit (M) from the supplier. 7. The retailer just offers a partial trade credit (N) to each customer i.e., the customer has to make an initial payment at the time of purchase and the remaining payment at the end of credit period (N). International Journal of Strategic Decision Sciences, 2(4), 61-74, October-December 2011 63 Copyright © 2011, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited. 8. During the credit period offered by the supplier, the retailer sells the items and uses the sales revenue to earn interest at a rate Ie. At the end of the permissible delay period, the retailer pays the purchasing cost to the supplier and incurs a capital opportunity cost at a rate Ip for the items in stock or for the items already sold but not yet paid for by the customers. In addition, following notation are used to develop the model: D(N,P) ≈D demand per unit of time Q order quantity T inventory cycle length I(t) the inventory level at time t A ordering cost per order C unit purchase price of the item P unit selling price of the item I inventory carrying charge per $ per unit time (excluding interest) Ie interest rate that can be earned Ip interest rate payable per $ per unit time a fraction of total amount payable by the customers to the retailer at the time of placing an order, 0 1 £ £ a M credit period offered by the supplier to the retailer N credit period offered by the retailer to his customers Z(T, P, N) retailer’s profit per unit time