Application Area B: Traffic and communication networks

Project B6

Origin destination control in airline revenue management by dynamic stochastic programming

Duration: |
July 2002 - May 2006 |

Project director: |
Prof. Dr. W. Römisch |

Department of Mathematics, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099 Berlin, Germany | |

Tel: +49 (0)30 - 2093 2561 (office) / - 2093 2353 (secretary) | |

email: romisch@mathematik.hu-berlin.de | |

Responsible: |
Dipl.-Math. Andris Möller |

Tel: +49 (0)30 - 2093 2262 (office) / - 2093 2353 (secretary) | |

email: andris@mathematik.hu-berlin.de | |

Cooperation: |
Lufthansa Systems Berlin |

Support: |
DFG Research Center "Mathematics for Key Technologies" |

A new dynamic stochastic programming model for origin destination control in airline revenue management is developed in [5], [6]. The new model will be compared with earlier approaches both by simulation studies and by investigating its structural and stability properties. Implications of these properties concern both essential ingredients of the algorithmic approach, namely, the construction of approximations of the multivariate booking demand processes and the design of solution algorithms (e.g. LP-based branch-and-cut, Lagrangian decomposition [3], [7]). Based on ideas in [1] and [2] we developed methods for constructing scenario trees from data scenarios in [4]. The whole solution procedure has been implemented and tested on real-life data of the stochastic booking demand of the company Lufthansa Systems Berlin.

[1] | J. Dupacova, N. Gröwe-Kuska and W. Römisch: |

Scenario reduction in stochastic programming: An approach using probability metrics. | |

Mathematical Programming Ser. A 95 (2003), 493-511. | |

[2] | N. Gröwe-Kuska, H. Heitsch and W. Römisch: |

Scenario reduction and scenario tree construction for power management problems. | |

IEEE Bologna Power Tech Proceedings (A. Borghetti, C.A. Nucci, M. Paolone eds.), 2003 IEEE. | |

[3] | D. Dentcheva and W. Römisch: |

Duality gaps in nonconvex stochastic optimization. | |

Mathematical Programming Ser. A 101 (2004), 515-535. | |

[4] | H. Heitsch and W. Römisch: |

Scenario tree modelling for multistage stochastic programs. | |

Preprint 296, DFG Research Center Matheon "Mathematics for key technologies", 2005 and submitted. | |

[5] | A. Möller, W. Römisch and K. Weber: |

A new approach to O&D revenue management based on scenario trees, | |

Journal of Revenue and Pricing Management 3 (2004), 265-276. | |

[6] | A. Möller, W. Römisch and K. Weber: |

Airline network revenue management by multistage stochastic programming, | |

Preprint 358, DFG Research Center Matheon "Mathematics for key technologies", 2006 and submitted. | |

[7] | W. Römisch and R. Schultz: |

Multistage stochastic integer programs: An introduction. | |

In: Online Optimization of Large Scale Systems (M. Grötschel, S.O. Krumke, J. Rambau eds.), Springer-Verlag, Berlin 2001, 579-598. |

last modified November 20, 2006