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An integer linear programming approach and a hybrid variable neighborhood search for the car sequencing problem

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  • Prandtstetter, Matthias
  • Raidl, Günther R.

Abstract

In this paper we present two major approaches to solve the car sequencing problem, in which the goal is to find an optimal arrangement of commissioned vehicles along a production line with respect to constraints of the form "no more than lc cars are allowed to require a component c in any subsequence of mc consecutive cars". The first method is an exact one based on integer linear programming (ILP). The second approach is hybrid: it uses ILP techniques within a general variable neighborhood search (VNS) framework for examining large neighborhoods. We tested the two methods on benchmark instances provided by CSPLIB and the automobile manufacturer RENAULT for the ROADEF Challenge 2005. These tests reveal that our approaches are competitive to previous reported algorithms. For the CSPLIB instances we were able to shorten the required computation time for reaching and proving optimality. Furthermore, we were able to obtain tight bounds on some of the ROADEF instances. For two of these instances the proposed ILP-method could provide new optimality proofs for already known solutions. For the VNS, the individual contributions of the used neighborhoods are also experimentally analyzed. Results highlight the significant impact of each structure. In particular the large ones examined using ILP techniques enhance the overall performance significantly, so that the hybrid approach clearly outperforms variants including only commonly defined neighborhoods.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:191:y:2008:i:3:p:1004-1022
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    References listed on IDEAS

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    1. M Gravel & C Gagné & W L Price, 2005. "Review and comparison of three methods for the solution of the car sequencing problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(11), pages 1287-1295, November.
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    Cited by:

    1. Raidl, Günther R., 2015. "Decomposition based hybrid metaheuristics," European Journal of Operational Research, Elsevier, vol. 244(1), pages 66-76.
    2. Heber F. Amaral & Sebastián Urrutia & Lars M. Hvattum, 2021. "Delayed improvement local search," Journal of Heuristics, Springer, vol. 27(5), pages 923-950, October.
    3. Mosadegh, H. & Fatemi Ghomi, S.M.T. & Süer, G.A., 2020. "Stochastic mixed-model assembly line sequencing problem: Mathematical modeling and Q-learning based simulated annealing hyper-heuristics," European Journal of Operational Research, Elsevier, vol. 282(2), pages 530-544.
    4. Felix Winter & Nysret Musliu, 2022. "A large neighborhood search approach for the paint shop scheduling problem," Journal of Scheduling, Springer, vol. 25(4), pages 453-475, August.
    5. Boysen, Nils & Scholl, Armin & Wopperer, Nico, 2012. "Resequencing of mixed-model assembly lines: Survey and research agenda," European Journal of Operational Research, Elsevier, vol. 216(3), pages 594-604.
    6. 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.
    7. Sioud, A. & Gagné, C., 2018. "Enhanced migrating birds optimization algorithm for the permutation flow shop problem with sequence dependent setup times," European Journal of Operational Research, Elsevier, vol. 264(1), pages 66-73.
    8. W. Jaśkowski & M. Szubert & P. Gawron, 2016. "A hybrid MIP-based large neighborhood search heuristic for solving the machine reassignment problem," Annals of Operations Research, Springer, vol. 242(1), pages 33-62, July.
    9. Elahi, Mirza M. Lutfe & Rajpurohit, Karthik & Rosenberger, Jay M. & Zaruba, Gergely & Priest, John, 2015. "Optimizing real-time vehicle sequencing of a paint shop conveyor system," Omega, Elsevier, vol. 55(C), pages 61-72.
    10. Marco Antonio Boschetti & Vittorio Maniezzo, 2022. "Matheuristics: using mathematics for heuristic design," 4OR, Springer, vol. 20(2), pages 173-208, June.
    11. Uli Golle & Franz Rothlauf & Nils Boysen, 2015. "Iterative beam search for car sequencing," Annals of Operations Research, Springer, vol. 226(1), pages 239-254, March.
    12. Pierre Hansen & Nenad Mladenović & José Moreno Pérez, 2010. "Variable neighbourhood search: methods and applications," Annals of Operations Research, Springer, vol. 175(1), pages 367-407, March.

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