Optimal seat allocation for two-flight problems with a flexible demand segment

In this paper, we study a two-flight model where there are two flights between two cities in a day (e.g., one departs at 9:00 am and another at 11:00 am) and booking requests in each fare class arrive according to a random process. There are three types of booking requests: the first and second types are respectively for the first and the second flight only; whereas the third type is flexible and willing to take either flight. Upon receiving a booking request, the airline has to decide whether to accept it, and in case a third type is accepted, which flight to accommodate it. This paper uncovers the structure of optimal booking policies through four monotone switching curves. We also present an extension of the basic model to multiple-flight case. Finally, a numerical example is used to illustrate the derivation and the dynamics of the optimal booking policies.