Efficient Algorithms for the Dynamic Pricing Problem with Reference Price Effect

• 成果类型: Article
• 署名作者: Chen, Xin; Hu, Peng; Hu, Zhenyu
• 署名单位: University of Illinois System; University of Illinois Urbana-Champaign; Huazhong University of Science & Technology; National University of Singapore
• 刊物名称: MANAGEMENT SCIENCE
• ISSN/ISSBN: 0025-1909
• DOI: 10.1287/mnsc.2016.2554
• 发表日期: 2017
• 页码: 4389-4408
• 关键词: Dynamic pricing; reference price effect; seasonality; dynamic programming; piecewise quadratic functions

摘要

We analyze a finite-horizon dynamic pricing model in which demand at each period depends on not only the current price but also past prices through reference prices. A unique feature but also a significant challenge in this model is the asymmetry in reference price effect, which implies that the underlying optimization problem is nonsmooth and no standard optimization methods can be applied. We identify a few key structural properties of the problem, which enable us to develop strongly polynomial-time algorithms to compute the optimal prices for several plausible scenarios. We complement our exact algorithms by proposing an approximation heuristic and provide an upper bound on the optimal objective value. Finally, we conduct numerical experiments to study the optimal price path and demonstrate the value of dynamic pricing when demands are seasonal. We further compare numerically one of the exact algorithms with the heuristic and offer managerial suggestions.