Dynamic Pricing Strategies in the Presence of Demand Shifts

We study the pricing problem of a retailer facing the prospect of a change in the demand function during a finite selling season with no inventory replenishment opportunity. In particular, the time and the form of change in demand are unknown upfront and we focus on the fundamental trade-off between collecting revenues from current demand and doing so for post-change demand, those being linked through the capacity constraint. We consider three representations of uncertainty about future demand, ranging from stochastic to adversarial views. Our analysis highlights the role dynamic pricing plays in hedging against future demand environments. Using a semi-deterministic relaxation, we show that optimal pricing strategies possess significant structure. When the time of change is independent of its form and a probabilistic description is available, we establish that the retailer can “order” the current and future demand environments to decide how to spread inventory consumption throughout the horizon. We further show that an optimal policy is always monotone up to a change and the direction of price changes depends on the aforementioned ordering. We establish that this structure extends to the case in which the time of change may be selected in an adversarial manner but not to the case in which both the time and form of a change may be selected in an adversarial fashion. In the latter case, time and form of change would in general be linked and optimal policies may be non-monotonic.