The Newsvendor Problem and Price-Only Contract When Bankruptcy Costs Exist
Article first published online: 13 DEC 2010
© 2010 Production and Operations Management Society
Production and Operations Management
Volume 20, Issue 6, pages 921–936, November/December 2011
How to Cite
Kouvelis, P. and Zhao, W. (2011), The Newsvendor Problem and Price-Only Contract When Bankruptcy Costs Exist. Production and Operations Management, 20: 921–936. doi: 10.1111/j.1937-5956.2010.01211.x
- Issue published online: 15 NOV 2011
- Article first published online: 13 DEC 2010
- History: Received: May 2009; Accepted: September 2010 by George Shanthikumar, after 2 revisions.
- wholesale price;
- bankruptcy risk;
- bankruptcy cost
We study a supply chain of a supplier selling via a wholesale price contract to a financially constrained retailer who faces stochastic demand. The retailer might need to borrow money from a bank to execute his order. The bank offers a fairly priced loan for relevant risks. Failure of loan repayment leads to a costly bankruptcy (fixed administrative costs, costs proportional to sales, and a depressed collateral value). We identify the retailer's optimal order quantity as a function of the wholesale price and his total wealth (working capital and collateral). The analysis of the supplier's optimal wholesale price problem as a Stackelberg game, with the supplier the leader and the retailer the follower, leads to unique equilibrium solutions in wholesale price and order quantity, with the equilibrium order quantity smaller than the traditional newsvendor one. Furthermore, in the presence of the retailer's bankruptcy risks, increases in the retailer's wealth lead to increased supplier's wholesale prices, but without the retailer's bankruptcy risks the supplier's wholesale prices stay the same or decrease in retailer's wealth.