Abstract
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.
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References
Shlifer, R., Vardi, Y.: An airline overbooking policy. Transp. Sci. 9(2), 101–114 (1975)
Liberman, V., Yechiali, U.: On the hotel overbooking problem - an inventory system with stochastic cancellations. Manage. Sci. 24(11), 1117–1126 (1978)
Chatwin, R.E.: Optimal control of continuous-time terminal-value birth-and-death processes and airline overbooking. Naval Res. Logist. 43(2), 159–168 (1996)
Chatwin, R.E.: Multi-period airline overbooking with a single fare class. Opns. Res. 46(6), 805–819 (1998)
Chatwin, R.E.: Continuous-time airline overbooking with time-dependent fares and refunds. Transp. Sci. 33(2), 182–191 (1999)
Fard, F.A., Sy, M., Ivanov, D.: Optimal overbooking strategies in the airlines using dynamic programming approach in continuous time. Transp. Res. Part E Logistics Transp. Rev. 128, 384–399 (2019)
Phillips, R.: Pricing and Revenue Optimization. Stanford University Press, Stanford (2005)
Sulima, N.: Probabilistic model of overbooking for an airline. Autom. Control Comput. Sci. 46(1), 68–78 (2012)
Kijima, M.: Total positivity. Markov Processes for Stochastic Modeling, pp. 313–318. Springer, Boston (1997). https://doi.org/10.1007/978-1-4899-3132-0_8
Pacheco, A., Tang, L.C., Prabhu, N.U.: Markov-Modulated Processes & Semiregenerative Phenomena. World Scientific, Hoboken, New York (2009)
Bellman, R.: Dynamic Programming. Princeton University Press, Princeton (1957)
Bellman, R.E., Dreyfus, S.E.: Applied Dynamic Programming. Princeton University Press, Princeton (1962)
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Andronov, A., Dalinger, I., Santalova, D. (2020). Problem of Overbooking for a Case of a Random Environment Existence. In: Vishnevskiy, V.M., Samouylov, K.E., Kozyrev, D.V. (eds) Distributed Computer and Communication Networks. DCCN 2020. Lecture Notes in Computer Science(), vol 12563. Springer, Cham. https://doi.org/10.1007/978-3-030-66471-8_30
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DOI: https://doi.org/10.1007/978-3-030-66471-8_30
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