American Institute of Mathematical Sciences

Advanced
  • Previous Article
    A nonmonotone smoothing Newton algorithm for solving box constrained variational inequalities with a $P_0$ function
  • JIMO Home
  • This Issue
  • Next Article
    Convergence property of an interior penalty approach to pricing American option
April  2011, 7(2): 449-465. doi: 10.3934/jimo.2011.7.449

Overbooking with transference option for flights

Yanming Ge 1, , Ziwen Yin 2, and  Yifan Xu 3,

1. 

School of management, Fudan University, Shanghai, 200433, China
2. 

School of management, Fudan University, Shanghai 200433, China
3. 

School of Management, Fudan University, Shanghai 200433

Received  February 2010 Revised  February 2011 Published  April 2011

In today's competitive market of the civil aviation industry, overbooking has been a common strategy for airlines to deal with uncertainty. However, while raising the overbooking level could recover partial losses caused by cancelation and no-show, this policy would bring more uncertainty into the system. As a solution, a new method of "transference" has recently been implemented by some major airlines in China. This method allows some of the overflowed passengers resulting from overbooking to board on a later flight with certain compensation. When it is properly implemented, airline companies could enjoy reduced uncertainty and improved revenue. In this paper, we build a model to depict this method, design a procedure to determine the optimal transferring quantity among flights of different departure times, analyze the overbooking level of each flight, and show improved revenue under the method of "transference". We also present a numerical example to highlight that our results may coincide with reality.
Keywords: transference, point process intensity control., overbooking, Revenue management.
Mathematics Subject Classification: Primary: 93E20, 90B06; Secondary: 49L2.
Citation: Yanming Ge, Ziwen Yin, Yifan Xu. Overbooking with transference option for flights. Journal of Industrial & Management Optimization, 2011, 7 (2) : 449-465. doi: 10.3934/jimo.2011.7.449
References:
[1]

J. Alstrup, S. Boas, O. B. G. Madsen and R. V. V. Vidal, Booking Policy for Flights with two types of passengers,, European Journal of Operational Research, 27 (1986), 274.  doi: 10.1016/0377-2217(86)90325-5.  Google Scholar

[2]

D. Arthur, S. Malone and O. Nir, Optimal overbooking,, The UMAP Journal, 23 (2002), 283.   Google Scholar

[3]

Y. Bassok, R. Anupindi and R. Akella, Single-period multiproduct inventory models with substitution,, Operations Research, 47 (1999), 632.  doi: 10.1287/opre.47.4.632.  Google Scholar

[4]

Z. P. Bayindir, N. Erkip and R. Güllü, Assessing the benefits of remanufacturing option under one-way substitution and capacity constraint,, Comput Oper Res, 34 (2007), 487.  doi: 10.1016/j.cor.2005.03.010.  Google Scholar

[5]

P. P. Belobaba, Airline Yield Management: An Overview of Seat Inventory Control,, Transportation Science, 21 (1987), 63.  doi: 10.1287/trsc.21.2.63.  Google Scholar

[6]

P. P. Belobaba, Application of a Probabilistic Decision Model to Airline Seat Inventory Control,, Operations Research, 37 (1989), 183.   Google Scholar

[7]

P. Brémaud, "Point Processes and Queues, Martingale Dynamics,", Springer-Verlag, (1981).   Google Scholar

[8]

T. Chatwin, Optimal control of continuous-time terminal-value birth-and-death processes and airline overbooking,, Naval Research Logistics, 43 (1996), 159.  doi: 10.1002/(SICI)1520-6750(199603)43:2<159::AID-NAV1>3.0.CO;2-9.  Google Scholar

[9]

R. E. Chatwin, Multi-period airline overbooking with a single fare class,, Operations Research, 46 (1998), 805.  doi: 10.1287/opre.46.6.805.  Google Scholar

[10]

R. E. Chatwin, Continuous-time airline overbooking with time dependent fares and refunds,, Transportation Science, 33 (1999), 182.  doi: 10.1287/trsc.33.2.182.  Google Scholar

[11]

Y. Feng and G. Gallego, Optimal stopping times for end of season sales and optimal starting times for promotional fares,, Management Science, 41 (1995), 1371.  doi: 10.1287/mnsc.41.8.1371.  Google Scholar

[12]

Y. Feng and B. Xiao, Maximizing revenue of perishable assets with risk analysis,, Operations Research, 47 (1999), 337.  doi: 10.1287/opre.47.2.337.  Google Scholar

[13]

Y. Feng and B. Xiao, Optimal policies of yield management with multiple predetermined prices,, Operations Research, 48 (2000), 332.  doi: 10.1287/opre.48.2.332.13373.  Google Scholar

[14]

Y. Gerchak, A. Tripathy and K. Wang, Co-procuction models with random functionality yields,, IIE Trans, 28 (1996), 391.  doi: 10.1080/07408179608966286.  Google Scholar

[15]

A. Hsu and Y. Bassok, Random yield and random demand in a production system with downward substitution,, Operations Research, 47 (1999), 277.  doi: 10.1287/opre.47.2.277.  Google Scholar

[16]

I. Karaesmen and G. van Ryzin, Overbooking with substitutable inventory classes,, Operations Research, 52 (2004), 83.  doi: 10.1287/opre.1030.0079.  Google Scholar

[17]

Z. L. Kevin, S. E. Spagniole and M. W. Stefan, Probabilistically optimized airline overbooking strategies, or "Anyone Willing to Take a Later Flight?!",, The UMAP Journal, 23 (2002), 317.   Google Scholar

[18]

L. Kosten, Een mathematisch model voor een reservingsprobleem,, Statist Neerlandica, 14 (1960), 85.  doi: 10.1111/j.1467-9574.1960.tb00893.x.  Google Scholar

[19]

Y. Liang, Solution to the continuous time dynamic yield management model,, Transportation Science, 33 (1999), 117.  doi: 10.1287/trsc.33.1.117.  Google Scholar

[20]

V. Liberman and U. Yechiali, On the hotel overbooking problem - an inventory system with stochastic cancellations,, Management Science, 24 (1978), 1117.  doi: 10.1287/mnsc.24.11.1117.  Google Scholar

[21]

K. Littlewood, Forecasting and control of passengers,, in, (1972), 103.   Google Scholar

[22]

M. Ignaccolo and G. Inturri, A Fuzz approach to overbooking in air transportation,, Journal of Air Transportation Worldwide, 5 (2000), 19.   Google Scholar

[23]

M. P. Schubmehl, W. M. Turner and D. M. Boylan, Models for evaluating airline overbooking,, The UMAP Journal, 23 (2002), 301.   Google Scholar

[24]

M. Rothstein, An airline Overbooking Model,, Transportation Science, 5 (1971), 180.  doi: 10.1287/trsc.5.2.180.  Google Scholar

[25]

B. Smith, J. Leimkuhler, R. Darrow and J. Samules, Yield management at american airlines,, Interface, 1 (1992), 8.   Google Scholar

[26]

J. Subramanian, S. Stidham and C. Lautenbacher, Airline yield management with overbooking, cancellation and no-shows,, Transportation Science, 33 (1999), 136.  doi: 10.1287/trsc.33.2.147.  Google Scholar

[27]

Y. Suzuki, An empirical analysis of the optimal overbooking policies for US major airlines,, Transportation Research Part E: Logistics and Transportation Review, 38 (2002), 135.  doi: 10.1016/S1366-5545(01)00016-3.  Google Scholar

[28]

Y. Suzuki, The net benefit of airline overbooking,, Transportation Research Part E: Logistics and Transportation Review, 42 (2006), 1.  doi: 10.1016/j.tre.2004.09.001.  Google Scholar

show all references

References:
[1]

J. Alstrup, S. Boas, O. B. G. Madsen and R. V. V. Vidal, Booking Policy for Flights with two types of passengers,, European Journal of Operational Research, 27 (1986), 274.  doi: 10.1016/0377-2217(86)90325-5.  Google Scholar

[2]

D. Arthur, S. Malone and O. Nir, Optimal overbooking,, The UMAP Journal, 23 (2002), 283.   Google Scholar

[3]

Y. Bassok, R. Anupindi and R. Akella, Single-period multiproduct inventory models with substitution,, Operations Research, 47 (1999), 632.  doi: 10.1287/opre.47.4.632.  Google Scholar

[4]

Z. P. Bayindir, N. Erkip and R. Güllü, Assessing the benefits of remanufacturing option under one-way substitution and capacity constraint,, Comput Oper Res, 34 (2007), 487.  doi: 10.1016/j.cor.2005.03.010.  Google Scholar

[5]

P. P. Belobaba, Airline Yield Management: An Overview of Seat Inventory Control,, Transportation Science, 21 (1987), 63.  doi: 10.1287/trsc.21.2.63.  Google Scholar

[6]

P. P. Belobaba, Application of a Probabilistic Decision Model to Airline Seat Inventory Control,, Operations Research, 37 (1989), 183.   Google Scholar

[7]

P. Brémaud, "Point Processes and Queues, Martingale Dynamics,", Springer-Verlag, (1981).   Google Scholar

[8]

T. Chatwin, Optimal control of continuous-time terminal-value birth-and-death processes and airline overbooking,, Naval Research Logistics, 43 (1996), 159.  doi: 10.1002/(SICI)1520-6750(199603)43:2<159::AID-NAV1>3.0.CO;2-9.  Google Scholar

[9]

R. E. Chatwin, Multi-period airline overbooking with a single fare class,, Operations Research, 46 (1998), 805.  doi: 10.1287/opre.46.6.805.  Google Scholar

[10]

R. E. Chatwin, Continuous-time airline overbooking with time dependent fares and refunds,, Transportation Science, 33 (1999), 182.  doi: 10.1287/trsc.33.2.182.  Google Scholar

[11]

Y. Feng and G. Gallego, Optimal stopping times for end of season sales and optimal starting times for promotional fares,, Management Science, 41 (1995), 1371.  doi: 10.1287/mnsc.41.8.1371.  Google Scholar

[12]

Y. Feng and B. Xiao, Maximizing revenue of perishable assets with risk analysis,, Operations Research, 47 (1999), 337.  doi: 10.1287/opre.47.2.337.  Google Scholar

[13]

Y. Feng and B. Xiao, Optimal policies of yield management with multiple predetermined prices,, Operations Research, 48 (2000), 332.  doi: 10.1287/opre.48.2.332.13373.  Google Scholar

[14]

Y. Gerchak, A. Tripathy and K. Wang, Co-procuction models with random functionality yields,, IIE Trans, 28 (1996), 391.  doi: 10.1080/07408179608966286.  Google Scholar

[15]

A. Hsu and Y. Bassok, Random yield and random demand in a production system with downward substitution,, Operations Research, 47 (1999), 277.  doi: 10.1287/opre.47.2.277.  Google Scholar

[16]

I. Karaesmen and G. van Ryzin, Overbooking with substitutable inventory classes,, Operations Research, 52 (2004), 83.  doi: 10.1287/opre.1030.0079.  Google Scholar

[17]

Z. L. Kevin, S. E. Spagniole and M. W. Stefan, Probabilistically optimized airline overbooking strategies, or "Anyone Willing to Take a Later Flight?!",, The UMAP Journal, 23 (2002), 317.   Google Scholar

[18]

L. Kosten, Een mathematisch model voor een reservingsprobleem,, Statist Neerlandica, 14 (1960), 85.  doi: 10.1111/j.1467-9574.1960.tb00893.x.  Google Scholar

[19]

Y. Liang, Solution to the continuous time dynamic yield management model,, Transportation Science, 33 (1999), 117.  doi: 10.1287/trsc.33.1.117.  Google Scholar

[20]

V. Liberman and U. Yechiali, On the hotel overbooking problem - an inventory system with stochastic cancellations,, Management Science, 24 (1978), 1117.  doi: 10.1287/mnsc.24.11.1117.  Google Scholar

[21]

K. Littlewood, Forecasting and control of passengers,, in, (1972), 103.   Google Scholar

[22]

M. Ignaccolo and G. Inturri, A Fuzz approach to overbooking in air transportation,, Journal of Air Transportation Worldwide, 5 (2000), 19.   Google Scholar

[23]

M. P. Schubmehl, W. M. Turner and D. M. Boylan, Models for evaluating airline overbooking,, The UMAP Journal, 23 (2002), 301.   Google Scholar

[24]

M. Rothstein, An airline Overbooking Model,, Transportation Science, 5 (1971), 180.  doi: 10.1287/trsc.5.2.180.  Google Scholar

[25]

B. Smith, J. Leimkuhler, R. Darrow and J. Samules, Yield management at american airlines,, Interface, 1 (1992), 8.   Google Scholar

[26]

J. Subramanian, S. Stidham and C. Lautenbacher, Airline yield management with overbooking, cancellation and no-shows,, Transportation Science, 33 (1999), 136.  doi: 10.1287/trsc.33.2.147.  Google Scholar

[27]

Y. Suzuki, An empirical analysis of the optimal overbooking policies for US major airlines,, Transportation Research Part E: Logistics and Transportation Review, 38 (2002), 135.  doi: 10.1016/S1366-5545(01)00016-3.  Google Scholar

[28]

Y. Suzuki, The net benefit of airline overbooking,, Transportation Research Part E: Logistics and Transportation Review, 42 (2006), 1.  doi: 10.1016/j.tre.2004.09.001.  Google Scholar

[1]

Sandeep Dulluri, N. R. Srinivasa Raghavan. Revenue management via multi-product available to promise. Journal of Industrial & Management Optimization, 2007, 3 (3) : 457-479. doi: 10.3934/jimo.2007.3.457
[2]

Karel Kadlec, Bohdan Maslowski. Ergodic boundary and point control for linear stochastic PDEs driven by a cylindrical Lévy process. Discrete & Continuous Dynamical Systems - B, 2017, 22 (11) : 0-0. doi: 10.3934/dcdsb.2020137
[3]

Hideaki Takagi. Extension of Littlewood's rule to the multi-period static revenue management model with standby customers. Journal of Industrial & Management Optimization, 2017, 13 (5) : 0-0. doi: 10.3934/jimo.2020064
[4]

Volker Rehbock, Iztok Livk. Optimal control of a batch crystallization process. Journal of Industrial & Management Optimization, 2007, 3 (3) : 585-596. doi: 10.3934/jimo.2007.3.585
[5]

Andrew J. Whittle, Suzanne Lenhart, Louis J. Gross. Optimal control for management of an invasive plant species. Mathematical Biosciences & Engineering, 2007, 4 (1) : 101-112. doi: 10.3934/mbe.2007.4.101
[6]

M. B. Short, G. O. Mohler, P. J. Brantingham, G. E. Tita. Gang rivalry dynamics via coupled point process networks. Discrete & Continuous Dynamical Systems - B, 2014, 19 (5) : 1459-1477. doi: 10.3934/dcdsb.2014.19.1459
[7]

Eungab Kim. On the admission control and demand management in a two-station tandem production system. Journal of Industrial & Management Optimization, 2011, 7 (1) : 1-18. doi: 10.3934/jimo.2011.7.1
[8]

Guirong Jiang, Qishao Lu, Linping Peng. Impulsive Ecological Control Of A Stage-Structured Pest Management System. Mathematical Biosciences & Engineering, 2005, 2 (2) : 329-344. doi: 10.3934/mbe.2005.2.329
[9]

C.E.M. Pearce, J. Piantadosi, P.G. Howlett. On an optimal control policy for stormwater management in two connected dams. Journal of Industrial & Management Optimization, 2007, 3 (2) : 313-320. doi: 10.3934/jimo.2007.3.313
[10]

Linhao Xu, Marya Claire Zdechlik, Melissa C. Smith, Min B. Rayamajhi, Don L. DeAngelis, Bo Zhang. Simulation of post-hurricane impact on invasive species with biological control management. Discrete & Continuous Dynamical Systems - A, 2020, 40 (6) : 4059-4071. doi: 10.3934/dcds.2020038
[11]

Valery Y. Glizer, Vladimir Turetsky, Emil Bashkansky. Statistical process control optimization with variable sampling interval and nonlinear expected loss. Journal of Industrial & Management Optimization, 2015, 11 (1) : 105-133. doi: 10.3934/jimo.2015.11.105
[12]

Xing Tan, Yilan Gu, Jimmy Xiangji Huang. An ontological account of flow-control components in BPMN process models. Big Data & Information Analytics, 2017, 2 (2) : 177-189. doi: 10.3934/bdia.2017016
[13]

Tan H. Cao, Boris S. Mordukhovich. Optimal control of a perturbed sweeping process via discrete approximations. Discrete & Continuous Dynamical Systems - B, 2016, 21 (10) : 3331-3358. doi: 10.3934/dcdsb.2016100
[14]

Ellina Grigorieva, Evgenii Khailov, Andrei Korobeinikov. Parametrization of the attainable set for a nonlinear control model of a biochemical process. Mathematical Biosciences & Engineering, 2013, 10 (4) : 1067-1094. doi: 10.3934/mbe.2013.10.1067
[15]

Lukáš Adam, Jiří Outrata. On optimal control of a sweeping process coupled with an ordinary differential equation. Discrete & Continuous Dynamical Systems - B, 2014, 19 (9) : 2709-2738. doi: 10.3934/dcdsb.2014.19.2709
[16]

Shaokuan Chen, Shanjian Tang. Semi-linear backward stochastic integral partial differential equations driven by a Brownian motion and a Poisson point process. Mathematical Control & Related Fields, 2015, 5 (3) : 401-434. doi: 10.3934/mcrf.2015.5.401
[17]

Yoon-Sik Cho, Aram Galstyan, P. Jeffrey Brantingham, George Tita. Latent self-exciting point process model for spatial-temporal networks. Discrete & Continuous Dynamical Systems - B, 2014, 19 (5) : 1335-1354. doi: 10.3934/dcdsb.2014.19.1335
[18]

Chanh Kieu, Quan Wang. On the scale dynamics of the tropical cyclone intensity. Discrete & Continuous Dynamical Systems - B, 2018, 23 (8) : 3047-3070. doi: 10.3934/dcdsb.2017196
[19]

Guangying Lv, Hongjun Gao, Jinlong Wei, Jiang-Lun Wu. The effect of noise intensity on parabolic equations. Discrete & Continuous Dynamical Systems - B, 2020, 25 (5) : 1715-1728. doi: 10.3934/dcdsb.2019248
[20]

Jose-Luis Roca-Gonzalez. Designing dynamical systems for security and defence network knowledge management. A case of study: Airport bird control falconers organizations. Discrete & Continuous Dynamical Systems - S, 2015, 8 (6) : 1311-1329. doi: 10.3934/dcdss.2015.8.1311

2018 Impact Factor: 1.025

Tools

Metrics

  • PDF downloads (46)
  • HTML views (0)
  • Cited by (2)

Other articles
by authors

[Back to Top]

Copyright © 2020 American Institute of Mathematical Sciences