Problem of Overbooking for a Case of a Random Environment Existence

摘要

An overbooking supposes that a booking of some product or service exceed given possibilities. It takes into consideration that a part of the booking will be cancelled. This situation is considered following to example of aviation ticket booking. It is supposed that an external random environment exists. The environment is described as a continuous-time finite irreducible Markov chain. A demand on the booking depends on the state of the random environment. An using of economical criterion supposes a consideration of such indices as costs of engaged seats of the aircraft and the penalty for the refusal of passenger with sold tickets. This criterion is optimized by means of dynamic programming method. A numerical example is considered.