Production cost functions and demand uncertainty effects in price-only contracts

Abstract

The price-only contract is the simplest and most common contract between a supplier and buyer in a supply chain. In such a contract, the supplier proposes a fixed wholesale price, and the buyer chooses a corresponding order quantity. The buyer’s optimal behavior is modeled using the Newsvendor model and the supplier’s optimal behavior is modeled as the solution to an optimization problem. This article explores, for the first time, the impact of general production costs on the supplier’s and buyer’s behavior. It is revealed that increased supplier’s production efficiency, reflected in lower marginal production costs, increases the buyer’s optimal profit. Therefore, a buyer would always prefer the more efficient supplier. A higher supplier efficiency, however, may or may not increase the supplier’s optimal profit, depending on the production function’s fixed costs. The effect of demand uncertainty, as measured by the coefficient of variation, is shown to increase the optimal order quantity. The uncertainty effect on the firms’ optimal profits is analyzed. Also, the relationship between production efficiency and the response to demand uncertainty is explored and it is shown that a higher efficiency level increases the responsiveness and volatility of the supplier’s production quantities. Thus, higher-efficiency suppliers are better positioned to respond to changes in the demand uncertainty in the supply chain.

Keywords:

• Production
• efficiency
• price-only contracts
• supply chain

Additional information

Notes on contributors

Dorit S. Hochbaum

Dorit S. Hochbaum is a Chancellor full professor at the University of California at Berkeley in Industrial Engineering and Operations Research (IEOR). Professor Hochbaum holds a Ph.D from the Wharton school of Business at the University of Pennsylvania. Her research interests are in the design and analysis of efficient algorithms, approximation algorithms, network flow–related problems, efficient utilization of resources, and discrete and continuous optimization. Her recent application areas of research relate to developing efficient methodologies for image segmentation, clustering, customer segmentation, prediction, ranking, group decision making and data mining. She has also investigated inverse problems, with applications varying from medical prognosis and error correction to financial risk assessment and prediction. Professor Hochbaum is the author of over 150 papers that appeared in the operations research, management science, and theoretical computer science literature. Professor Hochbaum was named in 2004 an honorary doctorate of Sciences of the University of Copenhagen for her work on approximation algorithms. In 2005 Professor Hochbaum was awarded the title of INFORMS fellow. She is the winner of the 2011 INFORMS Computing Society prize for her work on algorithms for image segmentation. In 2014 she was selected as a Fellow of the Society for Industrial and Applied Mathematics (SIAM).

Michael R. Wagner

Michael R. Wagner is an assistant professor of operations management at the Michael G. Foster School of Business at the University of Washington. His research interests are in decision making under uncertainty (stochastic, online, and robust optimization, as well as hybrids thereof). In particular, he investigates the value of information in a variety of application domains, such as supply chain management, inventory control, resource allocation, and logistics.