Analysis of Deterministic LP-Based Booking Limit and Bid Price Controls for Revenue Management

We study the performance of two popular and widely used heuristics for revenue management known as the booking limit and bid price controls. In contrast to a recent result in the literature where frequent re-solvings of a certain heuristic are shown to significantly reduce revenue loss, we show that the asymptotic revenue loss of either booking limit or bid price control cannot be reduced regardless of the choice of re-solving times and the frequency of re-solving. Moreover, we also show that further variations within the policy classes, such as nested instead of partition booking limit, or certainty equivalent instead of additive bid price, are simply indistinguishable in terms of their order of revenue loss under frequent re-solvings. This negative result highlights the limitation of re-solving deterministic linear programs when the solution is interpreted as either a booking limit or a bid price. Finally, we briefly discuss how to modify the traditional booking limit control to make it more responsive to frequent re-solvings and test its performance using numerical experiments.