Optimal booking control in revenue management with two substitutable resources

This paper studies optimal booking policies for capacity control models in revenue management with two substitutable resources. Our model covers a broader class of problems than previous works including (i)flexible demand and opaque selling for (ii)both dynamic and static demand settings. We provide a unifying characterization of the structure of optimal booking control by exploiting concavity, submodularity, and subconcavity of the value function. Our characterization is based on the notion of optimal booking paths formalizing the idea that an optimal allocation of a demand batch decomposes into a sequence of optimal single-request allocations. In addition, we examine the relationship between our booking path-based and a switching curve-based policy, which has been known previously for the case with dynamic demand. We show that both these characterizations describe an optimal policy. Computationally, there is no advantage of implementing either switching curves or booking paths in the dynamic setting. In the static setting, however, one can resort to the simple criteria which we propose in order to construct the optimal booking paths, thereby accelerating the evaluation of the value function.