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An Integer Programming Algorithm with Network Cuts for Solving the Assembly Line Balancing Problem

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  • F. Brian Talbot

    (University of Michigan)

  • James H. Patterson

    (University of Missouri---Columbia; Nijenrode, The Netherlands School of Business)

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    Abstract

    In this paper, we describe an integer programming algorithm for assigning tasks on an assembly line to work stations in such a way that the number of work stations is minimal for the rate of production desired. The procedure insures that no task is assigned to a work station before all tasks which technologically must be performed before it have been assigned (precedence restrictions are not violated), and that the total time required at each work station performing the tasks assigned to it does not exceed the time available (cycle time restrictions are not violated). The procedure is based on a systematic evaluation (enumeration) of all possible task assignments to work stations. Significant portions of the enumeration process are performed implicitly, however, by utilizing tests described in the paper which are based on the specific structure of the line balancing problem. An artifice termed a network cut is also developed which eliminates from explicit consideration the assignment of tasks to work stations where such assignments would not lead to improved line balances. Results reported demonstrate that the procedure can obtain optimal balances for assembly lines with between 50 and 100 tasks in a reasonable amount of computation time and with modest computer storage requirements.

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    File URL: http://dx.doi.org/10.1287/mnsc.30.1.85
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    Bibliographic Info

    Article provided by INFORMS in its journal Management Science.

    Volume (Year): 30 (1984)
    Issue (Month): 1 (January)
    Pages: 85-99

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    Handle: RePEc:inm:ormnsc:v:30:y:1984:i:1:p:85-99

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    Related research

    Keywords: production/scheduling: line balancing; programming: integer algorithms; enumerative; networks/graphs;

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    Cited by:
    1. Sawik, Tadeusz, 1998. "A lexicographic approach to bi-objective loading of a flexible assembly system," European Journal of Operational Research, Elsevier, vol. 107(3), pages 656-668, June.
    2. Chen, Ruey-Shun & Lu, Kun-Yung & Tai, Pei-Hao, 2004. "Optimizing assembly planning through a three-stage integrated approach," International Journal of Production Economics, Elsevier, vol. 88(3), pages 243-256, April.
    3. Miltenburg, John, 1998. "Balancing U-lines in a multiple U-line facility," European Journal of Operational Research, Elsevier, vol. 109(1), pages 1-23, August.
    4. 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.
    5. Armin Scholl & Christian Becker, 2003. "State-of-the-art exact and heuristic solution procedures for simple assembly line balancing," Jenaer Schriften zur Wirtschaftswissenschaft 20/2003, Friedrich-Schiller-Universit├Ąt Jena, Wirtschaftswissenschaftliche Fakult├Ąt.
    6. Scholl, Armin & Klein, Robert, 1999. "Balancing assembly lines effectively - A computational comparison," European Journal of Operational Research, Elsevier, vol. 114(1), pages 50-58, April.
    7. Pinnoi, Anulark & Wilhelm, Wilbert E., 2000. "Valid inequalities for a class of assembly system problems," European Journal of Operational Research, Elsevier, vol. 126(1), pages 31-50, October.

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