# Cooperative/Non-cooperative Supply Chain Models for Imperfect Quality Items with Trade Credit Financing

## Abstract

This paper studies the cooperative and non-cooperative models between the two partners of the supply chain system, seller and buyer. In this paper, supply chain models are formulated for imperfect quality items in which end demand of the product depends upon the retail price. The fixed credit period is offered by the seller to the buyer to stimulate his sales. The inspection process is also applied to each supplied lot at buyer’s end, and all the inspected items are separated into perfect quality items and imperfect quality items. Once the inspection process completed, perfect quality items are sold at selling price and imperfect quality items are sold at rebated/discounted price. The selling price and credit period proposed by the seller are considered as decision variables. The lot size and retailer price are decision variables of the buyer. In the proposed model, optimal policies of the seller’s and buyer’s are obtained under cooperative and non-cooperative analogue which will enhance the supply chain profit. Cooperative relationship is derived by a Pareto-efficient solution method, and non-cooperative is obtained by Seller-Stackelberg approach. Finally, numerical illustrations with sensibility analysis are stated to exemplify the theory of the paper.

## Keywords

Imperfect quality items Trade credit Game theory Non-cooperative game Cooperative games Supply chain## References

- 1.Haley CW, Higgins RC (1973) Inventory policy and trade credit financing. Manag Sci 20:464–471Google Scholar
- 2.Kim J, Hwang H, Shin S (1995) An optimal credit policy to increase supplier’s profits with price-dependent demand functions. Prod Plann Control 6:45–50Google Scholar
- 3.Hwang H, Shinn SW (1997) Retailer’s pricing and lot sizing policy for exponentially deteriorating products under the condition of permissible delay in payments. Comput Oper Res 24:539–547Google Scholar
- 4.Schwaller RL (1998) EOQ under inspection cost. Prod Inven Manag 29:22–24(1998)Google Scholar
- 5.Jamal AMM, Sarkar B, Wang S (2000) Optimal payment time for a retailer under permitted delay of payment to the wholesaler. Int J Prod Econ 66:59–66Google Scholar
- 6.Aggarwal SP, Jaggi CK (1995) Ordering policies of deteriorating items under permissible delay in payments. J Oper Res Soc 46:658–662Google Scholar
- 7.Jaggi CK, Goel SK, Mittal M (2011) Pricing and replenishment policies for imperfect quality deteriorating Items under Inflation and permissible delay in payments. Int J Strat Decis Sci 2:20–35Google Scholar
- 8.Thangam A, Uthaya kumar R (2009) Two-echelon trade credit financing for perishable items in a supply chain when demand depends on both selling price and credit period. Comput Ind Eng 57:773–786Google Scholar
- 9.Jaggi CK, Mittal M (2012) Retailer ordering policy for deteriorating items with initial inspection and allowable shortage under the condition of permissible delay in payments. Int J Appl Ind Eng 1:64–78Google Scholar
- 10.Zhou YW, Zhong YG, Li J (2012) An uncooperative order model for items with trade credit, inventory dependent demand and limited displayed-shelf space. Eur J Oper Res 223:76–85Google Scholar
- 11.Zhou Y, Chen C, Li C, Zhong Y (2016) A synergic economic order quantity model with trade credit, shortages, imperfect quality and inspection errors. Appl Math Model 40:1012–1028Google Scholar
- 12.Abad PL, Jaggi CK (2003) A Joint approach for setting unit price and length of the credit for a seller when end demand is price sensitive. Int J Prod Econ 83:115–122Google Scholar
- 13.Esmaeli M, Aryanezhad MB, Zeephongsekul P (2009) A game theory approach in seller buyer supply chain. Eur J Oper Res 195:442–448Google Scholar
- 14.Esmaeili M, Zeephongsekul P (2010) Seller buyer models of supply chain management with an asymmetric information structure. Int J Prod Econ 123:146–154Google Scholar
- 15.Zhang X, Zeephongsekul P (2013) Asymmetric information supply chain models with credit option. Ind Eng Manag Syst 12:264–273Google Scholar
- 16.Jaggi CK, Goel SK, Mittal M (2013) Credit financing in economic ordering policies for defective itemswith allowable shortages. Appl Math Comput 219:5268–5282Google Scholar
- 17.Maddah M, Jaber MY (2008) Economic order quantity for items with imperfect quality; revisited. Int J Prod Econ 112:808–815Google Scholar