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**A branch and bound algorithm for the two-stage assembly scheduling problem.**
*(English)*
Zbl 0921.90091

Summary: This paper develops a branch and bound algorithm for the two-stage assembly scheduling problem. In this problem, there are \(m\) machines at the first stage, each of which produces a component of a job. When all \(m\) components are available, a single assembly machine at the second stage completes the job. The objective is to schedule the jobs on the machines so that the maximum completion time, or makespan, is minimized. A lower bound based on solving an artificial two-machine flow shop problem is derived. Also, several dominance theorems are established and incorporated into the branch and bound algorithm. Computational experience with the algorithm is reported for problems with up to 8000 jobs and 10 first-stage machines.

### MSC:

90B35 | Deterministic scheduling theory in operations research |

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\textit{A. M. A. Hariri} and \textit{C. N. Potts}, Eur. J. Oper. Res. 103, No. 3, 547--556 (1997; Zbl 0921.90091)

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### References:

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[3] | Lee, C.-Y.; Cheng, T. C.E.; Lin, B. M.T., Minimizing the makespan in the 3-machine assembly-type flowshop scheduling problem, Management Science, 39, 616-625 (1993) · Zbl 0783.90054 |

[4] | Potts, C. N.; Sevast’janov, S. V.; Strusevich, V. A.; Van Wassenhove, L. N.; Zwaneveld, C. M., The two-stage assembly scheduling problem: complexity and approximation, Operations Research, 43, 346-355 (1995) · Zbl 0837.90069 |

[5] | Potts, C. N.; Van Wassenhove, L. N., An algorithm for single machine sequencing with deadlines to minimize total weighted completion time, European Journal of Operational Research, 12, 379-387 (1983) · Zbl 0496.90048 |

[6] | Potts, C. N.; Van Wassenhove, L. N., A branch and bound algorithm for the total weighted tardiness problem, Operations Research, 33, 363-377 (1985) · Zbl 0566.90046 |

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