Optimal dynamic pricing for deteriorating items with reference-price effects

Abstract

In this paper, a dynamic pricing problem for deteriorating items with the consumers’ reference-price effect is studied. An optimal control model is established to maximise the total profit, where the demand not only depends on the current price, but also is sensitive to the historical price. The continuous-time dynamic optimal pricing strategy with reference-price effect is obtained through solving the optimal control model on the basis of Pontryagin's maximum principle. In addition, numerical simulations and sensitivity analysis are carried out. Finally, some managerial suggestions that firm may adopt to formulate its pricing policy are proposed.

Keywords:

• dynamic pricing
• inventory control
• deteriorating items
• reference price
• optimal control

Additional information

Funding

This work was supported by the National Nature Science Foundation of China [grant number 71071106, 71371133, 61473204]; the Humanity and Social Science Youth Foundation of Ministry of Education of China [grant number 14YJCZH204]; the Program for New Century Excellent Talents in Universities of China [grant number NCET-11-0377].

Notes on contributors

Musen Xue

Musen Xue received his BS degree in information and computing science from Anhui University of Finance and Economics, Bengbu, China, in 2009, and his MS degree in logistics engineering from Tianjin University, Tianjin, China, in 2012. He is currently working toward his PhD degree under the supervision of Prof. Wansheng Tang at the Institute of Systems Engineering, Tianjin University, China. His current research interests include operations management and supply chain management.

Wansheng Tang

Wansheng Tang received his BS and MS degrees in operations research and control theory from Nankai University, Tianjin, China, in 1985 and 1988, respectively, and his PhD degree in systems engineering from Tianjin University, Tianjin, in 1993. He is currently a professor at the Institute of Systems Engineering, Tianjin University. His current research interests include modelling and control for complex systems, uncertain decision-making and job search theory.

Jianxiong Zhang

Jianxiong Zhang was born in Hunan province, China, in 1979. He received his BS degree in mechanical engineering and MS and PhD degrees in systems engineering from Tianjin University, Tianjin, China, in 2002, 2004 and 2006, respectively. He is currently a professor at the Institute of Systems Engineering, Tianjin University, Tianjin, China. His current research interests include dynamical supply chain management, modelling and control for complex systems. He has published more than 40 papers in journals like International Journal of Production Research, Journal of Optimization Theory and Applications, IEEE Transactions on Neural Networks, Neural Computation, Biological Cybernetics, Pattern Recognition, International Journal of Robust and Nonlinear Control, Nonlinear Dynamics and International Journal of Systems Science.