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Non-bottleneck machines in three-machine flow shops. (English) Zbl 0962.90017
Summary: The paper deals with the classical problem of minimizing the makespan in a three-machine flow shop. When any one of the three machines is a non-bottleneck machine, the problem is efficiently solvable by one of three algorithms from the literature. We show that even if one chooses the best solution, the worst-case performance ratio of these algorithms is 2, and the bound of 2 is tight. We also present a new sufficient condition for identifying the intermediate non-bottleneck machine which is weaker than all conditions proposed so far.

90B35 Deterministic scheduling theory in operations research
68Q25 Analysis of algorithms and problem complexity
Full Text: DOI
[9] Scheduling: Theory, Algorithms, and Systems. Prentice-Hall: Englewood Cliffs, NJ, 1995.
[17] Heuristic Scheduling Systems, With Applications to Production Systems and Project Management. Wiley: New York, 1993.
[21] Sequencing and scheduling: algorithms and complexity, In Handbooks in Operations Research and Management Science, Vol. 4, et al. (eds). North-Holland: Amsterdam, 1993.
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