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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. This paper was accepted by Yinyu Ye, optimization.
Chen et al. (Thu,) studied this question.