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

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  • Eivind Jahren

    (University of Bergen)

  • Roberto Asín Achá

    (Universidad de Concepción)

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.

Suggested Citation

  • Eivind Jahren & Roberto Asín Achá, 2018. "A column generation approach and new bounds for the car sequencing problem," Annals of Operations Research, Springer, vol. 264(1), pages 193-211, May.
    • Handle: RePEc:spr:annopr:v:264:y:2018:i:1:d:10.1007_s10479-017-2663-4
    DOI: 10.1007/s10479-017-2663-4
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    References listed on IDEAS

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    1. Estellon, Bertrand & Gardi, Frédéric & Nouioua, Karim, 2008. "Two local search approaches for solving real-life car sequencing problems," European Journal of Operational Research, Elsevier, vol. 191(3), pages 928-944, December.
    2. Prandtstetter, Matthias & Raidl, Günther R., 2008. "An integer linear programming approach and a hybrid variable neighborhood search for the car sequencing problem," European Journal of Operational Research, Elsevier, vol. 191(3), pages 1004-1022, December.
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    4. Solnon, Christine & Cung, Van Dat & Nguyen, Alain & Artigues, Christian, 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, Elsevier, vol. 191(3), pages 912-927, December.
    5. P. C. Gilmore & R. E. Gomory, 1961. "A Linear Programming Approach to the Cutting-Stock Problem," Operations Research, INFORMS, vol. 9(6), pages 849-859, December.
    6. Benoist, Thierry, 2008. "Soft car sequencing with colors: Lower bounds and optimality proofs," European Journal of Operational Research, Elsevier, vol. 191(3), pages 957-971, December.
    7. Cynthia Barnhart & Ellis L. Johnson & George L. Nemhauser & Martin W. P. Savelsbergh & Pamela H. Vance, 1998. "Branch-and-Price: Column Generation for Solving Huge Integer Programs," Operations Research, INFORMS, vol. 46(3), pages 316-329, June.
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