Annals of Operations Research

, Volume 264, Issue 1–2, pp 193–211 | Cite as

A column generation approach and new bounds for the car sequencing problem

Original Paper

Abstract

The subject of the 2005 ROADEF challenge was a variation of the car scheduling problem based on the needs of the Renaultfactories. In this paper we revisit this problem to investigate how further contributions can be made in order to close the gap between exact and heuristic methods that exists for this problem. For the benchmark set used in the final round of the competition we report new lower bounds for 7 out of the 19 instances by using an improved ILP formulation of the problem. We also present a new column generation based exact method for solving the ILP problem which outperforms branch-and-bound in obtaining upper bounds for these problems.

Keywords

Combinatorial optimization Industrial car sequencing Integer linear programming Column generation 

Notes

Acknowledgements

Roberto Asín’s research was funded by CONICYT, Chile, under FONDECYT project 11121220.

References

  1. Barnhart, C., Johnson, E. L., Nemhauser, G. L., Savelsbergh, M. W., & Vance, P. H. (1998). Branch-and-price: Column generation for solving huge integer programs. Operations Research, 46(3), 316–329.CrossRefGoogle Scholar
  2. Benoist, T. (2008). Soft car sequencing with colors: Lower bounds and optimality proofs. European Journal of Operational Research, 191(3), 957–971.CrossRefGoogle Scholar
  3. Biere, A. (2008). Adaptive restart control for conflict driven sat solvers. In Proceedings of SAT, 8.Google Scholar
  4. Briant, O., Naddef, D., & Mounié, G. (2008). Greedy approach and multi-criteria simulated annealing for the car sequencing problem. European Journal of Operational Research, 191(3), 993–1003.CrossRefGoogle Scholar
  5. Estellon, B., Gardi, F., & Nouioua, K. (2008). Two local search approaches for solving real-life car sequencing problems. European Journal of Operational Research, 191(3), 928–944.CrossRefGoogle Scholar
  6. Gilmore, P. C., & Gomory, R. E. (1961). A linear programming approach to the cutting-stock problem. Operations Research, 9(6), 849–859.CrossRefGoogle Scholar
  7. Gomes, C.P., Selman, B., & Kautz, H. (1998). Boosting combinatorial search through randomization.Google Scholar
  8. Gottlieb, J., Puchta, M., & Solnon, C. (2003) A study of greedy, local search, and ant colony optimization approaches for car sequencing problems. In Applications of evolutionary computing. Springer, pp. 246–257.Google Scholar
  9. Lee, J. H-M., Leung, H-F., & Won, H.-W. (1998). Performance of a comprehensive and efficient constraint library based on local search. In Advanced topics in artificial intelligence. Springer, pp. 191–202.Google Scholar
  10. Prandtstetter, M., & Raidl, G. (2005). A variable neighborhood search approach for solving the car sequencing problem. In Proceedings of the XVIII mini EURO conference on VNS.Google Scholar
  11. Prandtstetter, M., & Raidl, G. (2008). An integer linear programming approach and a hybrid variable neighborhood search for the car sequencing problem. European Journal of Operational Research, 191(3), 1004–1022.CrossRefGoogle Scholar
  12. Solnon, C., Cung, V. D., Nguyen, A., & Artigues, C. (2008). The car sequencing problem: Overview of state-of-the-art methods and industrial case-study of the roadef’2005 challenge problem. European Journal of Operational Research, 191(3), 912–927.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.Department of InformaticsUniversity of BergenBergenNorway
  2. 2.Computer Science DepartmentUniversidad de ConcepciónConcepciónChile

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