Performance of an LP-Based Control for Revenue Management with Unknown Demand Parameters

We consider a standard network revenue management (RM) problem and study the performance of a linear program (LP)-based control, the Probabilistic Allocation Control (PAC), in the presence of unknown demand parameters. We show that frequent re-optimizations of PAC without re-estimation suffice to shrink the asymptotic impact of estimation error on revenue loss. If, in addition to re-optimizations, we also frequently re-estimate the parameters, we prove that the performance of PAC in the unknown parameters setting is almost as good as the performance of PAC in the known parameters setting. Our numerical experiments show that PAC yields a revenue improvement of order 0.5%–1.5% relative to LP-based Booking Limit and Bid Price in most cases. Given the small margin in RM industries, such as the airline industry (about 2%), this level of improvement can easily translate into a significant increase in profit.