Efficient algorithms for the dynamic pricing problem with reference price effect

Xin Chen, Peng Hu, Zhenyu Hu

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)4389-4408
Number of pages20
JournalManagement Science
Issue number12
StatePublished - Dec 2017


  • Dynamic pricing
  • Dynamic programming
  • Piecewise quadratic functions
  • Reference price effect
  • Seasonality

ASJC Scopus subject areas

  • Strategy and Management
  • Management Science and Operations Research


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