| Summary: | We study a problem of dynamic pricing faced by a vendor with limited inventory, uncertain about the number of potential customers, aiming to maximize expected discounted revenue over an infinite time horizon. The vendor learns from purchase data, so his strategy must take into account the impact of price on both revenue and future observations. We focus on a model in which customers arrive according to a Poisson process, each with an independent, identically distributed reservation price. Upon arrival, a customer purchases a unit of inventory if his reservation price equals or exceeds the vendor’s prevailing price; otherwise, he exits the system. The vendor knows the reservation price distribution but not the customer arrival rate – for this he has a Gamma-distributed prior.
We propose a new heuristic approach to pricing, which we refer to as decay balancing. In the case where reservation prices are exponentially distributed, we prove that decay balancing always garners at least 33.3% of the maximum expected discounted revenue. Decay balancing appropriately increases price with arrival rate variance, in contrast to certainty equivalent and greedy heuristics, recently proposed by Aviv and Pazgal (2005) and Araman and Caldentey (2005), respectively. Further, computational experiments demonstrate that decay balancing offers significant revenue gains over these alternatives. We also extend the three aforementioned heuristics to address a model involving multiple customer segments and stores and provide experimental results demonstrating similar relative merits in this context. |
