IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v302y2022i2p589-605.html
   My bibliography  Save this article

Stochastic assembly line balancing: General bounds and reliability-based branch-and-bound algorithm

Author

Listed:
  • Diefenbach, Johannes
  • Stolletz, Raik

Abstract

We analyze the assembly line balancing problem with stochastic task times. Tasks have to be assigned to a minimum number of stations with a constraint on the line reliability, which is the probability of finishing a work piece completely. A sampling approach is developed that ensures the line reliability. We prove that any lower bound on the number of stations for the related deterministic problem can be transformed into a lower bound for this sampling formulation. This general transformation can be applied to any bound that has already been developed or to any potential new bound. Those bounds can be applied to any MIP model, optimization algorithm or heuristic procedure based on a sampling formulation. We exemplify the usefulness of these bounds in a reliability-based branch-and-bound (RB&B) algorithm that explicitly considers the dependence among all stations due to the constrained line reliability. A partial assignment of tasks to stations has to consider already constructed stations and potential further assignments to other stations. Hence, a feasible assignment of tasks to this station may allow for exceeding the cycle time with a certain probability but has to consider the overall line reliability with respect to the remaining stations. Effective fathoming strategies based on the new transformed lower bounds or based on a direct consideration of the line reliability are proposed. A numerical study shows that the transformed lower bounds are tight and that they substantially reduce the required computation times of the RB&B algorithm and of the solver CPLEX.

Suggested Citation

  • Diefenbach, Johannes & Stolletz, Raik, 2022. "Stochastic assembly line balancing: General bounds and reliability-based branch-and-bound algorithm," European Journal of Operational Research, Elsevier, vol. 302(2), pages 589-605.
  • Handle: RePEc:eee:ejores:v:302:y:2022:i:2:p:589-605
    DOI: 10.1016/j.ejor.2022.01.015
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221722000339
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.ejor.2022.01.015?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Boysen, Nils & Fliedner, Malte, 2008. "A versatile algorithm for assembly line balancing," European Journal of Operational Research, Elsevier, vol. 184(1), pages 39-56, January.
    2. Armin Scholl & Robert Klein, 1997. "SALOME: A Bidirectional Branch-and-Bound Procedure for Assembly Line Balancing," INFORMS Journal on Computing, INFORMS, vol. 9(4), pages 319-334, November.
    3. Mohand Lounes Bentaha & Olga Battaïa & Alexandre Dolgui, 2015. "An exact solution approach for disassembly line balancing problem under uncertainty of the task processing times," International Journal of Production Research, Taylor & Francis Journals, vol. 53(6), pages 1807-1818, March.
    4. Jordi Pereira, 2015. "Empirical evaluation of lower bounding methods for the simple assembly line balancing problem," International Journal of Production Research, Taylor & Francis Journals, vol. 53(11), pages 3327-3340, June.
    5. Pape, Tom, 2015. "Heuristics and lower bounds for the simple assembly line balancing problem type 1: Overview, computational tests and improvements," European Journal of Operational Research, Elsevier, vol. 240(1), pages 32-42.
    6. Urban, Timothy L. & Chiang, Wen-Chyuan, 2006. "An optimal piecewise-linear program for the U-line balancing problem with stochastic task times," European Journal of Operational Research, Elsevier, vol. 168(3), pages 771-782, February.
    7. Scholl, Armin & Becker, Christian, 2006. "State-of-the-art exact and heuristic solution procedures for simple assembly line balancing," European Journal of Operational Research, Elsevier, vol. 168(3), pages 666-693, February.
    8. Scholl, Armin & Klein, Robert, 1997. "SALOME. a bidirectional branch and bound procedure for assembly line balancing," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 7890, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    9. Franco Guerriero & John Miltenburg, 2003. "The stochastic U‐line balancing problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 50(1), pages 31-57, February.
    10. Robert L. Carraway, 1989. "A Dynamic Programming Approach to Stochastic Assembly Line Balancing," Management Science, INFORMS, vol. 35(4), pages 459-471, April.
    11. Moshe Sniedovich, 1981. "Analysis of a Preference Order Assembly Line Problem," Management Science, INFORMS, vol. 27(9), pages 1067-1080, September.
    12. Eren Özceylan & Can B. Kalayci & Aşkıner Güngör & Surendra M. Gupta, 2019. "Disassembly line balancing problem: a review of the state of the art and future directions," International Journal of Production Research, Taylor & Francis Journals, vol. 57(15-16), pages 4805-4827, August.
    13. Bentaha, Mohand Lounes & Battaïa, Olga & Dolgui, Alexandre & Hu, S. Jack, 2015. "Second order conic approximation for disassembly line design with joint probabilistic constraints," European Journal of Operational Research, Elsevier, vol. 247(3), pages 957-967.
    14. Sarin, Subhash C. & Erel, Erdal & Dar-El, Ezey M., 1999. "A methodology for solving single-model, stochastic assembly line balancing problem," Omega, Elsevier, vol. 27(5), pages 525-535, October.
    15. S D Lapierre & A B Ruiz, 2004. "Balancing assembly lines: an industrial case study," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(6), pages 589-597, June.
    16. Emel Kızılkaya Aydoğan & Yılmaz Delice & Uğur Özcan & Cevriye Gencer & Özkan Bali, 2019. "Balancing stochastic U-lines using particle swarm optimization," Journal of Intelligent Manufacturing, Springer, vol. 30(1), pages 97-111, January.
    17. Özcan, Ugur, 2010. "Balancing stochastic two-sided assembly lines: A chance-constrained, piecewise-linear, mixed integer program and a simulated annealing algorithm," European Journal of Operational Research, Elsevier, vol. 205(1), pages 81-97, August.
    18. Chiang, Wen-Chyuan & Urban, Timothy L., 2006. "The stochastic U-line balancing problem: A heuristic procedure," European Journal of Operational Research, Elsevier, vol. 175(3), pages 1767-1781, December.
    19. Daniel Leitold & Agnes Vathy-Fogarassy & Janos Abonyi, 2019. "Empirical working time distribution-based line balancing with integrated simulated annealing and dynamic programming," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 27(2), pages 455-473, June.
    20. Yılmaz Delice & Emel Kızılkaya Aydoğan & Uğur Özcan, 2016. "Stochastic two-sided U-type assembly line balancing: a genetic algorithm approach," International Journal of Production Research, Taylor & Francis Journals, vol. 54(11), pages 3429-3451, June.
    21. Otto, Alena & Otto, Christian & Scholl, Armin, 2013. "Systematic data generation and test design for solution algorithms on the example of SALBPGen for assembly line balancing," European Journal of Operational Research, Elsevier, vol. 228(1), pages 33-45.
    22. Jietao Dong & Linxuan Zhang & Tianyuan Xiao, 2018. "A hybrid PSO/SA algorithm for bi-criteria stochastic line balancing with flexible task times and zoning constraints," Journal of Intelligent Manufacturing, Springer, vol. 29(4), pages 737-751, April.
    23. Fred N. Silverman & John C. Carter, 1986. "A Cost-Based Methodology for Stochastic Line Balancing with Intermittent Line Stoppages," Management Science, INFORMS, vol. 32(4), pages 455-463, April.
    24. McMullen, Patrick R. & Frazier, Gregory V., 1997. "A heuristic for solving mixed-model line balancing problems with stochastic task durations and parallel stations," International Journal of Production Economics, Elsevier, vol. 51(3), pages 177-190, September.
    25. Wen-Chyuan Chiang & Timothy L. Urban & Chunyong Luo, 2016. "Balancing stochastic two-sided assembly lines," International Journal of Production Research, Taylor & Francis Journals, vol. 54(20), pages 6232-6250, October.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Boysen, Nils & Schulze, Philipp & Scholl, Armin, 2022. "Assembly line balancing: What happened in the last fifteen years?," European Journal of Operational Research, Elsevier, vol. 301(3), pages 797-814.
    2. Battaïa, Olga & Dolgui, Alexandre, 2022. "Hybridizations in line balancing problems: A comprehensive review on new trends and formulations," International Journal of Production Economics, Elsevier, vol. 250(C).
    3. Battaïa, Olga & Dolgui, Alexandre, 2013. "A taxonomy of line balancing problems and their solutionapproaches," International Journal of Production Economics, Elsevier, vol. 142(2), pages 259-277.
    4. Boysen, Nils & Fliedner, Malte & Scholl, Armin, 2007. "A classification of assembly line balancing problems," European Journal of Operational Research, Elsevier, vol. 183(2), pages 674-693, December.
    5. Becker, Christian & Scholl, Armin, 2006. "A survey on problems and methods in generalized assembly line balancing," European Journal of Operational Research, Elsevier, vol. 168(3), pages 694-715, February.
    6. Marcus Ritt & Alysson M. Costa & Cristóbal Miralles, 2016. "The assembly line worker assignment and balancing problem with stochastic worker availability," International Journal of Production Research, Taylor & Francis Journals, vol. 54(3), pages 907-922, February.
    7. Wen-Chyuan Chiang & Timothy L. Urban & Chunyong Luo, 2016. "Balancing stochastic two-sided assembly lines," International Journal of Production Research, Taylor & Francis Journals, vol. 54(20), pages 6232-6250, October.
    8. Pereira, Jordi & Álvarez-Miranda, Eduardo, 2018. "An exact approach for the robust assembly line balancing problem," Omega, Elsevier, vol. 78(C), pages 85-98.
    9. Bentaha, Mohand Lounes & Battaïa, Olga & Dolgui, Alexandre & Hu, S. Jack, 2015. "Second order conic approximation for disassembly line design with joint probabilistic constraints," European Journal of Operational Research, Elsevier, vol. 247(3), pages 957-967.
    10. Urban, Timothy L. & Chiang, Wen-Chyuan, 2016. "Designing energy-efficient serial production lines: The unpaced synchronous line-balancing problem," European Journal of Operational Research, Elsevier, vol. 248(3), pages 789-801.
    11. Scholl, Armin & Fliedner, Malte & Boysen, Nils, 2010. "Absalom: Balancing assembly lines with assignment restrictions," European Journal of Operational Research, Elsevier, vol. 200(3), pages 688-701, February.
    12. Raphael Kramer & Mauro Dell’Amico & Manuel Iori, 2017. "A batching-move iterated local search algorithm for the bin packing problem with generalized precedence constraints," International Journal of Production Research, Taylor & Francis Journals, vol. 55(21), pages 6288-6304, November.
    13. Lopes, Thiago Cantos & Pastre, Giuliano Vidal & Michels, Adalberto Sato & Magatão, Leandro, 2020. "Flexible multi-manned assembly line balancing problem: Model, heuristic procedure, and lower bounds for line length minimization," Omega, Elsevier, vol. 95(C).
    14. Daniel Leitold & Agnes Vathy-Fogarassy & Janos Abonyi, 2019. "Empirical working time distribution-based line balancing with integrated simulated annealing and dynamic programming," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 27(2), pages 455-473, June.
    15. Boysen, Nils & Fliedner, Malte, 2008. "A versatile algorithm for assembly line balancing," European Journal of Operational Research, Elsevier, vol. 184(1), pages 39-56, January.
    16. Özcan, Ugur, 2010. "Balancing stochastic two-sided assembly lines: A chance-constrained, piecewise-linear, mixed integer program and a simulated annealing algorithm," European Journal of Operational Research, Elsevier, vol. 205(1), pages 81-97, August.
    17. Boysen, Nils & Fliedner, Malte & Scholl, Armin, 2008. "Assembly line balancing: Which model to use when," International Journal of Production Economics, Elsevier, vol. 111(2), pages 509-528, February.
    18. Pape, Tom, 2015. "Heuristics and lower bounds for the simple assembly line balancing problem type 1: Overview, computational tests and improvements," European Journal of Operational Research, Elsevier, vol. 240(1), pages 32-42.
    19. Li, Zixiang & Kucukkoc, Ibrahim & Zhang, Zikai, 2020. "Branch, bound and remember algorithm for two-sided assembly line balancing problem," European Journal of Operational Research, Elsevier, vol. 284(3), pages 896-905.
    20. Sikora, Celso Gustavo Stall, 2024. "Balancing mixed-model assembly lines for random sequences," European Journal of Operational Research, Elsevier, vol. 314(2), pages 597-611.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ejores:v:302:y:2022:i:2:p:589-605. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.