Annals of Operations Research

, Volume 226, Issue 1, pp 239–254 | Cite as

Iterative beam search for car sequencing

  • Uli Golle
  • Franz Rothlauf
  • Nils Boysen


The car sequencing (CS) problem seeks a production sequence of different car models launched down a mixed-model assembly line. The models can be distinguished by selected options, e.g., sun roof yes/no. For every option, CS applies a so-called sequencing rule to avoid that consecutive models requiring this option lead to a work overload of the respective assembly operators. The aim is to find a sequence with minimum number of sequencing rule violations. This paper presents a graph representation of the problem and develops an exact solution approach based on iterative beam search. Furthermore, existing lower bounds are improved and applied. The experimental results reveal, that our solution approach is superior compared to the currently best known exact solution procedure. Our algorithm can even be applied as an efficient heuristic on problems of real-world size with up to 400 cars, where it shows competitive results compared to the current best known solutions.


Car sequencing Iterative beam search Mixed-model assembly lines 


  1. Bautista, J., Pereira, J., & Adenso-Diaz, B. (2008). A beam search approach for the optimization version of the car sequencing problem. Annals of Operations Research, 159, 233–244.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. Boysen, N., Fliedner, M., & Scholl, A. (2009). Sequencing mixed-model assembly lines: Survey, classification and model critique. European Journal of Operational Research, 192(2), 349–373.CrossRefGoogle Scholar
  4. Boysen, N., Golle, U., & Rothlauf, F. (2011). The car resequencing problem with pull-off tables. BuR - Business Research, 4(2), 1–17.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. Fliedner, M., & Boysen, N. (2008). Solving the car sequencing problem via branch & bound. European Journal of Operational Research, 191(3), 1023–1042.CrossRefGoogle Scholar
  7. Gagne, C., Gravel, M., & Price, W. (2006). Solving real car sequencing problems with ant colony optimization. European Journal of Operational Research, 174(3), 1427–1448.CrossRefGoogle Scholar
  8. Gent, I. P. (1998). Two results on car-sequencing problems. APES research report 02–1998. Glasgow: Department of Computer Science, University of Strathclyde.Google Scholar
  9. Gottlieb, J., Puchta, M., & Solnon, C. (2003). A study of greedy, local search, and ant colony optimization approaches for car sequencing problems. In S. Cagnoni, C. Johnson, J. Cardalda, E. Marchiori, D. Corne, J. A. Meyer, J. Gottlieb, M. Middendorf, A. Guillot, G. Raidl, & E. Hart (Eds.), EvoWorkshops 2003, LNCS 2611 (pp. 246–257). Berlin Heidelberg: Springer.Google Scholar
  10. Gravel, M., Gagne, C., & Price, W. L. (2005). Review and comparison of three methods for the solution of the car sequencing problem. Journal of the Operational Research Society, 56(11), 1287–1295.CrossRefGoogle Scholar
  11. Jaszkiewicz, A., Kominek, P., & Kubiak, M. (2004). Adaptation of the genetic local search algorithm to a car sequencing problem. In 7th National conference on evolutionary algorithms and global optimization. Kazimierz Dolny, Poland, pp. 67–74.Google Scholar
  12. Kis, T. (2004). On the complexity of the car sequencing problem. Operations Research Letters, 32(4), 331–335.CrossRefGoogle Scholar
  13. Klein, R., & Scholl, A. (1999). Scattered branch and bound: An adaptive search strategy applied to resource-constrained project scheduling. Central European Journal of Operations Research, 7, 177–201.Google Scholar
  14. Lowerre, B. (1976). The harpy speech recognition system. Ph.D. thesis, Carnegie Mellon University, Pittsburgh, USA.Google Scholar
  15. Parrello, B. D., Kabat, W. C., & Wos, L. (1986). Job-shop scheduling using automated reasoning: A case study of the car-sequencing problem. Journal of Automated Reasoning, 2(1), 1–42.CrossRefGoogle Scholar
  16. Perron, L., & Shaw, P. (2004). Combining forces to solve the car sequencing problem. In J. C. Regin & M. Rueher (Eds.), Integration of AI and OR techniques in constraint programming for combinatorial optimization problems, LNCS 3011 (pp. 225–239). Berlin Heidelberg: Springer.CrossRefGoogle Scholar
  17. 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
  18. Puchta, M. & Gottlieb, J. (2002). Solving car sequencing problems by local optimization. In Proceedings of the applications of evolutionary computing on evoworkshops 2002, LNCS, Vol. 2279 (pp. 132–142). Berlin, Heidelberg: Springer.Google Scholar
  19. Solnon, C., Cung, V., 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
  20. Warwick, T., & Tsang, E. (1995). Tackling car sequencing problems using a generic genetic algorithm. Evolutionary Computation, 3(3), 267–298.CrossRefGoogle Scholar
  21. Wester, L. & Kilbridge, M. D. (1964). The assembly line model-mix sequencing problem. In Proceedings of the Third International Conference on Operations Research.Google Scholar
  22. Zinflou, A., Gagne, C., & Gravel, M. (2007). Crossover operators for the car sequencing problem. In C. Cotta & J. van Hemert (Eds.), Proceedings of the 7th European conference on evolutionary computation in combinatorial optimization, EvoCOP 2007, LNCS (Vol. 4446, pp. 229–239). Valencia, Spain.Google Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Lehrstuhl für Wirtschaftsinformatik und BWLJohannes Gutenberg-Universität MainzMainzGermany
  2. 2.Lehrstuhl für Operations ManagementFriedrich-Schiller-Universität JenaJenaGermany

Personalised recommendations