Summary
Crew pairing problems are often solved using column generation in a branch-and-price framework. The main idea of this approach consists of solving linear programming relaxations for a subset of variables and employing pricing for introducing additional variables with negative reduced costs. Since the dual variables are not bounded, this leads to instability in the standard implementation of this method. Therefore, a so-called stabilized column generation with respective control parameters is suggested to overcome this problem by reducing the number of redundant variables. In this paper we report about possible realizations of this principle and show that the performance of algorithms can be improved significantly.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
P. Alefragis, C. Goumopoulos, E. Housos, P. Sanders, T. Takkula, and D. Wedelin. Parallel Crew Scheduling in PAROS. In Proceedings of Euro-Par'98 Parallel Processing: 4th International Euro-Par Conference, 1998.
C. Barnhart, E. L. Johnson, G. L. Nemhauser, M. W. P. Savelsbergh, and P. H. Vance. Branch-and-price: Column Generation for Solving Huge Integer Programs. Operations Research, 46:316–329, 1998.
J. Desrosiers, Y. Dumas, M. M. Solomon, and F. Soumis. Handbooks in Operations Research and Management Science, volume 8, chapter Time Constrained Routing and Scheduling, pages 35–139. North-Holland, 1993.
O. du Merle, D. Villeneuve, J. Desrosiers, and P. Hansen. Stabilized Column Generation. Discrete Mathematics, 194:229–237, 1999.
N. Guerinik and M. V. Caneghem. Solving Crew Scheduling Problems by Constraint Programming. In Proceedings of the ist Conference of Principles and Practice of Constraint Programming, pages 481–498, 1995.
T. Gustafsson. A Heuristic Approach to Column Generation for Airline Crew Scheduling. PhD thesis, Chalmers University of Technology, 1999.
I. Ioachim, S. GAlinas, F. Soumis, and J. Desrosiers. A Dynamic Programming for the Shortest Path Problem with Time Windows and Linear Node Costs. Networks, 31, 1997.
B. Jaumard, F. Semet, and T. Vovor. A Two-Phase Resource Constrained Shortest Path Algorithm for Acyclic Graphs. Technical report, Les Cahiers du GERAD, 1999.
J. E. Kelley. The Cutting Plane Method for Solving Convex Program. Journal of SIAM, 8:703–712, 1960.
D. Klabjan and K. Schwan. Airline Crew Pairing Generation in Parallel. Technical report, The Logistics Institute, Georgia institute of Technology, 1999.
R. E. Marsten, W. W. Hogan, and J. W. Blankenship. The Boxstep Method for Large-Scale Optimization. Operations Research, 23(3):389–405, 1975.
P. J. Neame. Nonsmooth Dual Methods in Integer Programming. PhD thesis, The University of Melbourne, 1999.
P. H. Vance, A. Atamtürk, C. Barnhart, E. Gelman, E. L. Johnson, A. Krishna, D. Mahidhara, and R. Rebello. A Heuristic Branch-and-Price Approach for the Airline Crew Pairing Problem, 1997.
R. Wunderling. SoPlex, The Sequential Object-Oriented Simplex Class Library. ZIB, 1997.
T. H. Yunes, A. V. Moura, and C. C. de Souza. Practical Aspects of Declarative Languages, volume 1753 of Lecture notes in computer science, chapter A Hybrid Approach for Solving Large Scale Crew Scheduling Problems, pages 293–307. Springer, 2000.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Van Hoai, T., Reinelt, G., Bock, H.G. (2005). Advanced Column Generation Techniques for Crew Pairing Problems. In: Bock, H.G., Phu, H.X., Kostina, E., Rannacher, R. (eds) Modeling, Simulation and Optimization of Complex Processes. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-27170-8_16
Download citation
DOI: https://doi.org/10.1007/3-540-27170-8_16
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-23027-4
Online ISBN: 978-3-540-27170-3
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)