Nash and integrated solutions in a just-in-time seller–buyer supply chain with buyer's ordering cost reductions

Abstract

The seller frequently offers the buyer trade credit to settle the purchase amount. From the seller's prospective, granting trade credit increases not only the opportunity cost (i.e., the interest loss on the buyer's purchase amount during the credit period) but also the default risk (i.e., the rate that the buyer will be unable to pay off his/her debt obligations). On the other hand, granting trade credit increases sales volume and revenue. Consequently, trade credit is an important strategy to increase seller's profitability. In this paper, we assume that the seller uses trade credit and number of shipments in a production run as decision variables to maximise his/her profit, while the buyer determines his/her replenishment cycle time and capital investment as decision variables to reduce his/her ordering cost and achieve his/her maximum profit. We then derive non-cooperative Nash solution and cooperative integrated solution in a just-in-time inventory system, in which granting trade credit increases not only the demand but also the opportunity cost and default risk, and the relationship between the capital investment and the ordering cost reduction is logarithmic. Then, we use a software to solve and compare these two distinct solutions. Finally, we use sensitivity analysis to obtain some managerial insights.

Keywords:

• inventory
• trade credit
• Nash solution
• integrated solution
• just-in-time
• order cost reduction

Acknowledgements

The authors would like to thank editor-in-chief P.J. Fleming, an associate editor, and three anonymous referees for their constructive comments, and Professor Y.L. Chan for helping us revise Figure 1.

Additional information

Notes on contributors

Kuo-Ren Lou

Kuo-Ren Lou is currently an associate professor in the Department of Management Sciences at Tamkang University in Taiwan. He received his PhD degree in the Department of Statistics from the University of Connecticut, CT, USA. His research interests are in statistics, operations research, and sampling methods. His publications appear in European Journal of Operational Research, International Journal of Production Economics, Applied Mathematics and Computation, Journal of Global Optimization, International Journal of Systems Science, TOP, and Statistics & Decisions.

Lu Wang

Lu Wang is a PhD student in the Department of Management Sciences, Tamkang University, Taiwan. She was an MS in Management from Graduate Institute of Management Sciences, Tamkang University, Taiwan,and a BS in the Department of Applied English from the University of Kang Ning, Taiwan. Her interests include stock management and supply chain management.