Parametric demand learning with limited price explorations in a backlog stochastic inventory system

Abstract

We study a multi-period stochastic inventory system with backlogs. Demand in each period is random and price sensitive, but the firm has little or no prior knowledge about the demand distribution and how each customer responds to the selling price, so the firm has to learn the demand process when making periodic pricing and inventory replenishment decisions to maximize its expected total profit. We consider the scenario where the firm is faced with the business constraint that prevents it from conducting extensive price exploration, and develop parametric data-driven algorithms for pricing and inventory decisions. We measure the performances of the algorithms by regret, which is the profit loss compared with a clairvoyant who has complete information about the demand distribution. We analyze the cases where the number of price changes is restricted to a given number or a small number relative to the planning horizon, and show that the regrets for the corresponding learning algorithms converge at the best possible rates in the sense that they reach the theoretical lower bounds. Numerical results indicate that these algorithms empirically perform very well. Supplementary materials are available for this article. Go to the publisher’s online edition of IISE Transaction, for datasets, additional tables, detailed proofs, etc.

Keywords:

• Backlog inventory control
• parametric demand learning
• limited price exploration
• asymptotic optimality

Acknowledgment

The authors are grateful to the Area Editor and the two referees for their helpful comments and suggestions that have helped to significantly improve the exposition of this paper.

Additional information

Funding

The research of Xiuli Chao is supported by the NSF under grant CMMI-1634676.

Notes of Contributors

Boxiao Chen is an assistant professor at the College of Business Administration, University of Illinois at Chicago. Her research focuses on data-driven optimization with applications in revenue management, inventory control, and supply chain management. She holds doctoral degree in industrial and operations engineering from University of Michigan, Ann Arbor.

Xiuli Chao is a professor in the Department of Industrial and Operations Engineering at the University of Michigan, Ann Arbor. His recent research interests include stochastic modeling and analysis, inventory control, data-driven optimization, game analysis, and supply chain management. Xiuli Chao is the co-developer of the Lekin Scheduling System, and is the co-author of two books, “Operations Scheduling with Applications in Manufacturing and Services” (Irwin/McGraw-Hill, 1998), and “Queueing Networks: Customers, Signals, and Product Form Solutions” (John Wiley & Sons, 1999). Chao shared the Erlang Prize from the Applied Probability Society of INFORMS in 1998, and he received the David F. Baker Distinguished Research Award from the Institute of Industrial and Systems Engineers (IISE) in 2005. He holds doctoral degree in operations research from Columbia University.