Non-Cooperative Game Theoretic Approach in Supply Chain With Imperfect Quality Items and Credit Financing

Non-Cooperative Game Theoretic Approach in Supply Chain With Imperfect Quality Items and Credit Financing

Rita Yadav (Apaji Institute of Mathematics and Applied Computer Technology, India), Sarla Pareek (Apaji Institute of Mathematics and Applied Computer Technology, India) and Mandeep Mittal (Amity School of Engineering and Technology, India)
DOI: 10.4018/978-1-5225-3232-3.ch013


This paper considers a supply chain model for imperfect quality items in which retail price of the buyer influences the demand of the product. The seller offers fix credit period for the buyer to stimulate his sales. Each delivered lot, goes through an inspection process at the buyer's end. After the inspection, items are separated into two parts, one is perfect quality items and another is imperfect quality items. The perfect quality items are sold at selling price and the imperfect items are sold at a discounted price immediately after the inspection process. The credit period offered by the seller and the selling price of the seller, both are considered as a decision variable. Relationship between seller and buyer is derived from the non-cooperative Seller- Stackelberg game approach. Optimal selling price, credit period and order quantity are determined by maximizing expected total profit of the supply chain. At the end, numerical examples with sensitivity analysis are given to explain the theory of the paper.
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Game Theory studies the interactive optimization problems in which the decisions of multiple players affect each other’s profit. This theory plays a vital role in the field of supply chain channel, whose objective is to develop supply chain policies with various assumptions and with different perspectives which not only improve coordination between the various channels in the supply chain, but also achieving the best outcomes efficiently. In this paper, seller sent the item to the buyer, but in real situations, certain items are not of perfect quality. Thus, the inspection of received lot becomes an essential part at the buyer’s end for all the items. Initially, Schwaller (1988) studied EOQ models on defective items by considering inspection cost. Wee et al. (2007) explored an optimal inventory model for imperfect quality items with the case of shortage backordering. They too built up an algorithm to present their better results.

Now a day’s credit period policy are used by most of the supply chain industries to increase their sales to improve the profit of supply chain members. The trade Credit policy is an endorsed settlement between buyer and seller for delayed payment. It is generally offered to the buyer by the seller. Many authors worked on credit financing for best results such as Haley and Higgins (1973) studied the buyer’s lot sizing problems under a trade credit period with the constant demand. Kim et al. (1995) developed a model to determine the optimal trade credit period with the assumption that the selling price of the seller is fixed.

Zhang and Gerchak (1990) studied lot sizing and inspection policy together with random yields. Hwang and Shinn (1997) studied that when demand is price sensitive then the lot size is variant with respect to the length of credit period. Aggarwal and Jaggi (1995) and Jamal et al. (2000) studied under the fixed demand, the deteriorating item problems with permissible delay in payment. Jaber and Osman (2006) studied a supply chain model in which they proposed a policy in which the seller used trade credit to increase the order quantity of the buyer and will charge interest for the delay in payments. Jaggi et al. (2011) determined policies for Imperfect quality deteriorating Items related to pricing and replenishment under allowable delay in payments and Inflation, when the market demand depends upon the selling price of the buyer. Chen and Kang (2010) explained an integrated production-inventory model for a two-stage supply chain in which demand rate of the customer is assumed to be selling price sensitive .The inventory models are developed, and then optimal values of the selling price, order quantity and number of shipments for the independent and also joint supply chain are determined. The effects of the parameters of the model on the performance of the supply chain are investigated.

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