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The maximum length car sequencing problem

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  • Pontes, Lara
  • Neves, Carlos
  • Subramanian, Anand
  • Battarra, Maria

Abstract

This paper introduces the maximum length car sequencing problem to support the assembly operations of a multinational automotive company. We propose an integer linear programming (ILP) formulation to schedule the maximum number of cars without violating the so-called option constraints. In addition, we present valid combinatorial lower and upper bounds, which can be calculated in less than 0.01 s, as well as binary and iterative search algorithms to solve the problem when good primal bounds are not readily available. To quickly obtain high-quality solutions, we devise an effective iterated local search algorithm, and we use the heuristic solutions as warm start to further enhance the performance of the exact methods. Computational results demonstrate that relatively low gaps were achieved for benchmark instances within a time limit of ten minutes. We also conducted an instance space analysis to identify the features that make the problem more difficult to solve. Moreover, the instances reflecting the company’s needs could be solved to optimality in less than a second. Finally, simulations with real-world demands, divided into shifts, were conducted over a period of four months. In this case, we use the proposed ILP model in all shifts except the last one of each month, for which we employ an alternative ILP model to sequence the unscheduled cars, adjusting the pace of the assembly line in an optimal fashion. The results pointed out that the latter was necessary in only one of the months.

Suggested Citation

  • Pontes, Lara & Neves, Carlos & Subramanian, Anand & Battarra, Maria, 2024. "The maximum length car sequencing problem," European Journal of Operational Research, Elsevier, vol. 316(2), pages 707-717.
  • Handle: RePEc:eee:ejores:v:316:y:2024:i:2:p:707-717
    DOI: 10.1016/j.ejor.2024.02.024
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    References listed on IDEAS

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    1. 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.
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    5. 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.
    6. Boysen, Nils & Fliedner, Malte & Scholl, Armin, 2009. "Sequencing mixed-model assembly lines: Survey, classification and model critique," European Journal of Operational Research, Elsevier, vol. 192(2), pages 349-373, January.
    7. 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.
    8. Fliedner, Malte & Boysen, Nils, 2008. "Solving the car sequencing problem via Branch & Bound," European Journal of Operational Research, Elsevier, vol. 191(3), pages 1023-1042, December.
    9. Dhananjay Thiruvady & Kerri Morgan & Amiza Amir & Andreas T. Ernst, 2020. "Large neighbourhood search based on mixed integer programming and ant colony optimisation for car sequencing," International Journal of Production Research, Taylor & Francis Journals, vol. 58(9), pages 2696-2711, May.
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    11. Joaquín Bautista & Jordi Pereira & Belarmino Adenso-Díaz, 2008. "A Beam Search approach for the optimization version of the Car Sequencing Problem," Annals of Operations Research, Springer, vol. 159(1), pages 233-244, March.
    12. Ribeiro, Celso C. & Aloise, Daniel & Noronha, Thiago F. & Rocha, Caroline & Urrutia, Sebastián, 2008. "A hybrid heuristic for a multi-objective real-life car sequencing problem with painting and assembly line constraints," European Journal of Operational Research, Elsevier, vol. 191(3), pages 981-992, December.
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