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Bounds for Assembly Line Balancing Heuristics

Author

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  • Maurice Queyranne

    (The University of British Columbia, Vancouver, British Columbia)

Abstract

We analyze the asymptotic worst-case performance ratio of polynomial time heuristics for the assembly line balancing problem. Assuming that P ≠ NP , we show that no polynomial heuristic has worst-case ratio less than 1.5. (This ratio is known to be not worse than 2 for any “reasonable” heuristic.) Tighter results are established for problems with only “short” tasks, i.e., when all processing times do not exceed a given fraction of the cycle time. These results apply even to planar, series-parallel precedence constraints, and contrast with known results for situations with an empty precedence relation, i.e., the bin packing problem. In particular, if P ≠ NP , there are no fully polynomial approximation schemes for assembly line balancing, even with “short” tasks and planar, series-parallel precedence constraints.

Suggested Citation

  • Maurice Queyranne, 1985. "Bounds for Assembly Line Balancing Heuristics," Operations Research, INFORMS, vol. 33(6), pages 1353-1359, December.
    • Handle: RePEc:inm:oropre:v:33:y:1985:i:6:p:1353-1359
    DOI: 10.1287/opre.33.6.1353
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    Cited by:

    1. Santiago Valdés Ravelo, 2022. "Approximation algorithms for simple assembly line balancing problems," Journal of Combinatorial Optimization, Springer, vol. 43(2), pages 432-443, March.
    2. Amen, Matthias, 2001. "Heuristic methods for cost-oriented assembly line balancing: A comparison on solution quality and computing time," International Journal of Production Economics, Elsevier, vol. 69(3), pages 255-264, February.
    3. 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.

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