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A Branch and Bound Algorithm for Assembly Line Balancing Problems with Formulation Irregularities

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  • Roger V. Johnson

    (University of California at Los Angeles)

Abstract

This paper describes a branch and bound algorithm which can solve assembly line balancing probems with nine modifications to the originally formulated problem of minimizing the required number of assembly stations, given a cycle time, a set of tasks with given deterministic performance times, and between-task precedence relationships. The first two formulation modifications are those of permitting planned imbalance in the total of task performance times at each assembly station, and allowing specific tasks to be assigned to specific types of assembly stations. Seven further problem modifications can be solved by the proposed algorithm, or by any algorithm or heuristic that can solve problems containing these first two modifications. They are: treatment of stochastic task performance times on unpaced lines; requirement of particular tasks to be assigned to particular stations; requirement of task groupings according to task skill levels; requirement of particular tasks to be assigned to only a left-of-line or right-of line station; required task separations; some mixed model situations; and where paralleling of a specified task into two (or more stations) is permitted. The algorithm is presented in both conceptual and detailed form. Computer computation times to solve a selected cross-sectional sample of problems are provided.

Suggested Citation

  • Roger V. Johnson, 1983. "A Branch and Bound Algorithm for Assembly Line Balancing Problems with Formulation Irregularities," Management Science, INFORMS, vol. 29(11), pages 1309-1324, November.
    • Handle: RePEc:inm:ormnsc:v:29:y:1983:i:11:p:1309-1324
    DOI: 10.1287/mnsc.29.11.1309
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    Cited by:

    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. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. van Zante-de Fokkert, Jannet I. & de Kok, Ton G., 1997. "The mixed and multi model line balancing problem: a comparison," European Journal of Operational Research, Elsevier, vol. 100(3), pages 399-412, August.
    9. 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.
    10. Fatih Ugurdag, H. & Rachamadugu, Ram & Papachristou, Christos A., 1997. "Designing paced assembly lines with fixed number of stations," European Journal of Operational Research, Elsevier, vol. 102(3), pages 488-501, November.
    11. 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.
    12. Lopes, Thiago Cantos & Michels, Adalberto Sato & Sikora, Celso Gustavo Stall & Molina, Rafael Gobbi & Magatão, Leandro, 2018. "Balancing and cyclically sequencing synchronous, asynchronous, and hybrid unpaced assembly lines," International Journal of Production Economics, Elsevier, vol. 203(C), pages 216-224.

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