Joint pricing and inventory control for a stochastic inventory system with Brownian motion demand

ABSTRACT

In this article, we consider an infinite horizon, continuous-review, stochastic inventory system in which the cumulative customers’ demand is price dependent and is modeled as a Brownian motion. Excess demand is backlogged. The revenue is earned by selling products and the costs are incurred by holding/shortage and ordering; the latter consists of a fixed cost and a proportional cost. Our objective is to simultaneously determine a pricing strategy and an inventory control strategy to maximize the expected long-run average profit. Specifically, the pricing strategy provides the price p_t for any time t ⩾ 0 and the inventory control strategy characterizes when and how much we need to order. We show that an (s*, S*, p*) policy is optimal and obtain the equations of optimal policy parameters, where p* = {p*_t: t ⩾ 0}. Furthermore, we find that at each time t, the optimal price p*_t depends on the current inventory level z, and it is increasing in [s*, z*] and decreasing in [z*, ∞), where z* is a negative level.

KEYWORDS:

• Stochastic inventory model
• pricing
• Brownian motion demand
• (s, S, p) policy
• impulse control
• drift rate control

Acknowledgements

The author thanks the Department Editor, the Associate Editor, and the anonymous referees for their thoughtful comments and suggestions, which have helped to significantly improve this article. The author thanks Ping Cao from University of Science and Technology of China, Xin Chen from University of Illinois at Urbana--Champaign, Shuangchi He from National University of Singapore, and Guodong Pang from Pennsylvania State University for their useful comments.

Funding

The work was supported in part by the National Natural Science Foundation of China under grants 11401566 and 11771432.

Additional information

Notes on contributors

Dacheng Yao

Dacheng Yao is an Associate Professor at the Academy of Mathematics and Systems Science, Chinese Academy of Sciences. His research interests include inventory control, stochastic models, and applied probability. He received a B.Sc. degree in information and computing science from the Shandong University in 2005 and a Ph.D. degree in operational research and cybernetics from the Chinese Academy of Sciences in 2010. He held a postdoctoral position at the Chinese Academy of Sciences from 2010 to 2012. He has held visiting positions at the Georgia Institute of Technology, the National University of Singapore, and the Chinese University of Hong Kong.