IDEAS home Printed from https://ideas.repec.org/a/eee/jomega/v78y2018icp57-68.html
   My bibliography  Save this article

Constraint programming for solving various assembly line balancing problems

Author

Listed:
  • Bukchin, Yossi
  • Raviv, Tal

Abstract

In this paper, the constraint programming (CP) approach is applied for the simple assembly line balancing problem (SALBP) as well as some of its generalizations. CP is a rich modeling language that enables the formulation of general combinatorial problems and is coupled with a strong set of solution methods that are available through general purpose solvers. The proposed formulations are conversions of well-known mixed integer programming (MILP) formulations to CP, along with a new set of constraints that helps the CP solver to converge faster. As a generic solution method, we compare its performance with the best known generic MILP formulations and show that it consistently outperforms MILP for medium to large problem instances. A comparison with SALOME, a well-known custom-made algorithm for solving the SALBP-1, shows that both approaches are capable of efficiently solving problems with up to 100 tasks. When 1000-task problems are concerned, SALOME provides better performance; however, CP can provide relatively good close to optimal solutions for multiple combinations of problem parameters. Finally, the generality of the CP approach is demonstrated by some adaptations of the proposed formulation to other variants of the assembly line balancing problem including the U-shaped assembly line balancing problem and the task assignment and equipment selection problem.

Suggested Citation

  • Bukchin, Yossi & Raviv, Tal, 2018. "Constraint programming for solving various assembly line balancing problems," Omega, Elsevier, vol. 78(C), pages 57-68.
    • Handle: RePEc:eee:jomega:v:78:y:2018:i:c:p:57-68
    DOI: 10.1016/j.omega.2017.06.008
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0305048316306363
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.omega.2017.06.008?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. 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.
    2. F. Brian Talbot & James H. Patterson, 1984. "An Integer Programming Algorithm with Network Cuts for Solving the Assembly Line Balancing Problem," Management Science, INFORMS, vol. 30(1), pages 85-99, January.
    3. E. C. Sewell & S. H. Jacobson, 2012. "A Branch, Bound, and Remember Algorithm for the Simple Assembly Line Balancing Problem," INFORMS Journal on Computing, INFORMS, vol. 24(3), pages 433-442, August.
    4. 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.
    5. Scholl, Armin, 1995. "Balancing and sequencing of assembly lines," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 9690, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    6. G. J. Miltenburg & J. Wijngaard, 1994. "The U-line Line Balancing Problem," Management Science, INFORMS, vol. 40(10), pages 1378-1388, October.
    7. E. H. Bowman, 1960. "Assembly-Line Balancing by Linear Programming," Operations Research, INFORMS, vol. 8(3), pages 385-389, June.
    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. William W. White, 1961. "Letter to the Editor---Comments on a Paper by Bowman," Operations Research, INFORMS, vol. 9(2), pages 274-276, April.
    10. Michael Held & Richard M. Karp & Richard Shareshian, 1963. "Assembly-Line Balancing---Dynamic Programming with Precedence Constraints," Operations Research, INFORMS, vol. 11(3), pages 442-459, June.
    11. Morrison, David R. & Sewell, Edward C. & Jacobson, Sheldon H., 2014. "An application of the branch, bound, and remember algorithm to a new simple assembly line balancing dataset," European Journal of Operational Research, Elsevier, vol. 236(2), pages 403-409.
    12. Roger V. Johnson, 1988. "Optimally Balancing Large Assembly Lines with "Fable"," Management Science, INFORMS, vol. 34(2), pages 240-253, February.
    13. Amen, Matthias, 2006. "Cost-oriented assembly line balancing: Model formulations, solution difficulty, upper and lower bounds," European Journal of Operational Research, Elsevier, vol. 168(3), pages 747-770, February.
    14. James H. Patterson & Joseph J. Albracht, 1975. "Technical Note—Assembly-Line Balancing: Zero-One Programming with Fibonacci Search," Operations Research, INFORMS, vol. 23(1), pages 166-172, February.
    15. Linus Schrage & Kenneth R. Baker, 1978. "Dynamic Programming Solution of Sequencing Problems with Precedence Constraints," Operations Research, INFORMS, vol. 26(3), pages 444-449, June.
    16. Timothy L. Urban, 1998. "Note. Optimal Balancing of U-Shaped Assembly Lines," Management Science, INFORMS, vol. 44(5), pages 738-741, May.
    17. 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.
    18. Thomas R. Hoffmann, 1992. "Eureka: A Hybrid System for Assembly Line Balancing," Management Science, INFORMS, vol. 38(1), pages 39-47, January.
    19. 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.
    20. James R. Jackson, 1956. "A Computing Procedure for a Line Balancing Problem," Management Science, INFORMS, vol. 2(3), pages 261-271, April.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Jiménez-Piqueras, Celia & Ruiz, Rubén & Parreño-Torres, Consuelo & Alvarez-Valdes, Ramon, 2023. "A constraint programming approach for the premarshalling problem," European Journal of Operational Research, Elsevier, vol. 306(2), pages 668-678.
    2. Zhu, Xuedong & Son, Junbo & Zhang, Xi & Wu, Jianguo, 2023. "Constraint programming and logic-based Benders decomposition for the integrated process planning and scheduling problem," Omega, Elsevier, vol. 117(C).
    3. Mao, Zhaofang & Sun, Yiting & Fang, Kan & Huang, Dian & Zhang, Jiaxin, 2024. "Balancing and scheduling of assembly line with multi-type collaborative robots," International Journal of Production Economics, Elsevier, vol. 271(C).
    4. Schmid, Nico André & Limère, Veronique & Raa, Birger, 2021. "Mixed model assembly line feeding with discrete location assignments and variable station space," Omega, Elsevier, vol. 102(C).
    5. Hassan Zohali & Bahman Naderi & Vahid Roshanaei, 2022. "Solving the Type-2 Assembly Line Balancing with Setups Using Logic-Based Benders Decomposition," INFORMS Journal on Computing, INFORMS, vol. 34(1), pages 315-332, January.
    6. Hashemi-Petroodi, S. Ehsan & Thevenin, Simon & Kovalev, Sergey & Dolgui, Alexandre, 2022. "Model-dependent task assignment in multi-manned mixed-model assembly lines with walking workers," Omega, Elsevier, vol. 113(C).
    7. 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.
    8. Xujing Zhang & Yan Chen, 2019. "Carbon Emission Evaluation Based on Multi-Objective Balance of Sewing Assembly Line in Apparel Industry," Energies, MDPI, vol. 12(14), pages 1-19, July.
    9. 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).
    10. Koltai, Tamás & Dimény, Imre & Gallina, Viola & Gaal, Alexander & Sepe, Chiara, 2021. "An analysis of task assignment and cycle times when robots are added to human-operated assembly lines, using mathematical programming models," International Journal of Production Economics, Elsevier, vol. 242(C).
    11. Bahman Naderi & Rubén Ruiz & Vahid Roshanaei, 2023. "Mixed-Integer Programming vs. Constraint Programming for Shop Scheduling Problems: New Results and Outlook," INFORMS Journal on Computing, INFORMS, vol. 35(4), pages 817-843, July.
    12. Fatemi-Anaraki, Soroush & Tavakkoli-Moghaddam, Reza & Foumani, Mehdi & Vahedi-Nouri, Behdin, 2023. "Scheduling of Multi-Robot Job Shop Systems in Dynamic Environments: Mixed-Integer Linear Programming and Constraint Programming Approaches," Omega, Elsevier, vol. 115(C).
    13. Bukchin, Yossi & Raviv, Tal & Zaides, Ilya, 2020. "The consecutive multiprocessor job scheduling problem," European Journal of Operational Research, Elsevier, vol. 284(2), pages 427-438.
    14. Eduardo Álvarez-Miranda & Jordi Pereira & Harold Torrez-Meruvia & Mariona Vilà, 2021. "A Hybrid Genetic Algorithm for the Simple Assembly Line Balancing Problem with a Fixed Number of Workstations," Mathematics, MDPI, vol. 9(17), pages 1-19, September.
    15. Barzanji, Ramin & Naderi, Bahman & Begen, Mehmet A., 2020. "Decomposition algorithms for the integrated process planning and scheduling problem," Omega, Elsevier, vol. 93(C).

    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, 2013. "A taxonomy of line balancing problems and their solutionapproaches," International Journal of Production Economics, Elsevier, vol. 142(2), pages 259-277.
    3. Walter, Rico & Schulze, Philipp & Scholl, Armin, 2021. "SALSA: Combining branch-and-bound with dynamic programming to smoothen workloads in simple assembly line balancing," European Journal of Operational Research, Elsevier, vol. 295(3), pages 857-873.
    4. Sprecher, Arno, 2000. "SALBLIB: Challenging instances for assembly line balancing," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 526, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    5. Vilà, Mariona & Pereira, Jordi, 2013. "An enumeration procedure for the assembly line balancing problem based on branching by non-decreasing idle time," European Journal of Operational Research, Elsevier, vol. 229(1), pages 106-113.
    6. 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.
    7. Schulze, Philipp & Scholl, Armin & Walter, Rico, 2024. "R-SALSA: A branch, bound, and remember algorithm for the workload smoothing problem on simple assembly lines," European Journal of Operational Research, Elsevier, vol. 312(1), pages 38-55.
    8. 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.
    9. Bautista, Joaquín & Pereira, Jordi, 2011. "Procedures for the Time and Space constrained Assembly Line Balancing Problem," European Journal of Operational Research, Elsevier, vol. 212(3), pages 473-481, August.
    10. 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.
    11. Armin Scholl & Nils Boysen & Malte Fliedner, 2009. "Optimally solving the alternative subgraphs assembly line balancing problem," Annals of Operations Research, Springer, vol. 172(1), pages 243-258, November.
    12. 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.
    13. Aase, Gerald R. & Olson, John R. & Schniederjans, Marc J., 2004. "U-shaped assembly line layouts and their impact on labor productivity: An experimental study," European Journal of Operational Research, Elsevier, vol. 156(3), pages 698-711, August.
    14. 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.
    15. Morrison, David R. & Sewell, Edward C. & Jacobson, Sheldon H., 2014. "An application of the branch, bound, and remember algorithm to a new simple assembly line balancing dataset," European Journal of Operational Research, Elsevier, vol. 236(2), pages 403-409.
    16. Bautista, Joaquín & Pereira, Jordi, 2009. "A dynamic programming based heuristic for the assembly line balancing problem," European Journal of Operational Research, Elsevier, vol. 194(3), pages 787-794, May.
    17. Sprecher, Arno, 1997. "A competitive exact algorithm for assembly line balancing," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 449, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    18. Becker, Christian & Scholl, Armin, 2009. "Balancing assembly lines with variable parallel workplaces: Problem definition and effective solution procedure," European Journal of Operational Research, Elsevier, vol. 199(2), pages 359-374, December.
    19. Klein, Robert & Scholl, Armin, 1996. "Maximizing the production rate in simple assembly line balancing -- A branch and bound procedure," European Journal of Operational Research, Elsevier, vol. 91(2), pages 367-385, June.
    20. 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.

    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:jomega:v:78:y:2018:i:c:p:57-68. 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/wps/find/journaldescription.cws_home/375/description#description .

    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.