| When a customer requests a discount fare, the airline must decide whether to sell the seat at the requested discount or to hold the seat in hope that a customer will arrive later who will pay more. I model this situation for a single leg flight with multiple fare classes and customers who arrive according to a semi-Markov process (possibly nonhomogeneous). These customers can request multiple seats (batch requests) and can be overbooked. Under certain conditions, I show that the value function decreases as departure approaches. If each customer only requests a single seat or if the requests can be partially satisfied, then I show that there are optimal booking curves which decrease as departure approaches. I provide counterexamples to show that this structural property of the optimal policy does not hold in general. When customers are allowed to cancel I show that booking curves exist and may be monotone in certain cases.; I also consider the situation where the customer's request size and fare offered are not known, but their joint probability distribution is available, and show that under certain conditions existence of booking curves obtains, and that under further assumptions, they are monotone. Finally, the theoretical results are used in realistic numerical examples, which are compared to certain deterministic upper bounds and revenues obtained under heuristic policies.; The airline yield management problem described above is an instance of a generic revenue management problem, which, in turn, can be cast into a finite horizon semi-Markov dynamic optimal control problem. I provide examples of other applications of revenue management. |
