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Assembly-Line Balancing---Dynamic Programming with Precedence Constraints

Author

Listed:
  • Michael Held

    (International Business Machines Corporation, New York, New York)

  • Richard M. Karp

    (International Business Machines Corporation, New York, New York)

  • Richard Shareshian

    (International Business Machines Corporation, New York, New York)

Abstract

This paper approaches the assembly-line balancing problem as a sequencing problem involving precedence constraints that prohibit the occurrence of certain orderings. This approach permits the formulation of a dynamic programming algorithm for the exact solution of small assembly-line balancing problems. A generalization of this algorithm combined with a successive approximations technique is used for the solution of large problems. In addition, certain combinatorial problems associated with partially ordered sets are formulated and discussed in detail. These problems arise whenever sequencing problems with precedence constraints are treated by dynamic programming techniques.

Suggested Citation

  • 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.
  • Handle: RePEc:inm:oropre:v:11:y:1963:i:3:p:442-459
    DOI: 10.1287/opre.11.3.442
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    Citations

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    Cited by:

    1. 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.
    2. 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.
    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. 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.
    5. Bukchin, Yossi & Raviv, Tal, 2018. "Constraint programming for solving various assembly line balancing problems," Omega, Elsevier, vol. 78(C), pages 57-68.
    6. 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.
    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. 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.

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