An inventory system with quasi-hyperbolic discounting rate

ABSTRACT

In this article, we consider a periodic-review inventory system with stochastic demands for an infinite horizon, where the manager has a time-inconsistent preference with a quasi-hyperbolic discounting rate. We model the inventory system as an intra-personal sequential decision problem. It is shown that the ordering decision follows a base-stock policy but has a systematic bias in that the base-stock level is lower than the standard optimal level. We extend our analysis to a supply chain that is composed of a perfectly rational supplier and a quasi-hyperbolic retailer. The results show that the time-inconsistent preference of the retailer can cause considerable loss in system performance. We propose a contract with a delay-in-payment and income-sharing for such a supply chain. The results show that the contract can effectively un-bias the ordering decision of the retailer and can reach the goal of coordinating the supply chain to improve the performance.

KEYWORDS:

• Inventory
• quasi-hyperbolic discount
• base-stock policy
• delay-in-payment
• supply chain coordination

Funding

This research is supported by the National Science Foundation (NSF) of China under grant 71210002 and partially supported by the NSF of China under grant 71671099.

Additional information

Notes on contributors

Xiaobo Zhao

Xiaobo Zhao is a Professor in Department of Industrial Engineering, Tsinghua University, China. He received a B.S. from Dalian Railway Institute in 1983, M.S. from Wuhan University of Technology in 1988, and a Ph.D. from Nagoya Institute of Technology (Japan) in 1996. His research interests cover modeling and analysis of operations management, including supply chain management, queueing systems, production management, and behavioral operations management. He has published papers in leading journals such as Management Science, Operations Research, Mathematics of Operations Research, Production and Operations Management, Naval Research Logistics, as well as IISE Transactions.

Yun Zhou

Yun Zhou is currently a Ph.D. candidate at the Rotman School of Management, University of Toronto. His research interests include inventory management, revenue management, and healthcare operations management. Most recently, his research has focused on operational problems in the sharing economy. Before his studies at the University of Toronto, he studied at the Department of Industrial Engineering and Department of Mathematical Sciences in Tsinghua University.

Jinxing Xie

Jinxing Xie is a professor in the Department of Mathematical Sciences, Tsinghua University, China. He received a B.Sc. degree in applied mathematics in 1988 and a Ph.D. in computational mathematics in 1995, both from Tsinghua University. He has the experience of working at Shanghai Baoshan Steel Group as a production planning and scheduling engineer for 2 years (1988–1990). His current research interests lie in the fields of logistics and supply chain management. His work appears in academic journals including Operations Research, Decision Sciences, Production and Operations Management, Naval Research Logistics, European Journal of Operational Research, Journal of the Operational Research Society, and Omega.