Overbooking for parallel flights with transference

Abstract

This paper considers a dynamic overbooking problem for parallel substitutable flights with different departure times. Those flights have multiple fare classes, and reservations are allowed to be canceled with costs. If the go-shows of a flight are larger than its capacity, then some of them may be transferred to a later flight if it has enough capacity. We separate the whole system into some subsystems according to their departure times. The analysis of each sub-system is divided into two parts. The first part derives the optimal booking rules under a given terminal function. The second part determines the terminal function of this subsystem according to a capacity allocation optimization scheme. The optimizing terminal function is shown to be well structured. The optimal overbooking control is conducted by setting overbooking limits on each flight in subsystem dynamically. The terminal function is inherited by the value function of the underlying continuous-time Markov decision process which takes it as the terminal reward. The upper bound on the overbooking limits of each flight is numerically computable, which confines the procedure of computing dynamic overbooking limits to finite ranges.