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The Two-Machine Flow Shop

In: Flow Shop Scheduling

Author

Listed:
  • Hamilton Emmons

    (Case Western Reserve University)

  • George Vairaktarakis

    (Case Western Reserve University)

Abstract

The two-machine flow shop has attracted significant attention, especially when it comes to extensions of the basic makespan model to include release times, setups, or other complications. As expected, we start our coverage with a full discussion of Johnson’s Rule for makespan minimization. Then, we present extensions that incorporate setup/teardown times in automated manufacturing cells. When arbitrary positive release times are assumed for jobs, the problem of minimizing makespan in the two-machine flow shop is shown to be NPcomplete, and hence we discuss solution procedures, optimal and heuristic. Even when a single server is used to perform setups, the problem is shown strongly NP-complete, though special cases accept simple solutions. Results on optimal lot streaming of a product are also presented. Precedence constraints are postponed to a later chapter. Subsequently, we survey results on objectives like ΣCj, Lmax, Tmax, ΣTj, ΣUj, as well as corresponding multicriteria. Various manifestations of these models come with setups, scarce resources, common deadlines, etc. Whenever possible, we provide dominance properties, lower bounds, branch-andbound approaches, heuristics and computational results.

Suggested Citation

  • Hamilton Emmons & George Vairaktarakis, 2013. "The Two-Machine Flow Shop," International Series in Operations Research & Management Science, in: Flow Shop Scheduling, edition 127, chapter 0, pages 21-66, Springer.
    • Handle: RePEc:spr:isochp:978-1-4614-5152-5_2
    DOI: 10.1007/978-1-4614-5152-5_2
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    Cited by:

    1. Vahid Nasrollahi & Ghasem Moslehi & Mohammad Reisi-Nafchi, 2022. "Minimizing the weighted sum of maximum earliness and maximum tardiness in a single-agent and two-agent form of a two-machine flow shop scheduling problem," Operational Research, Springer, vol. 22(2), pages 1403-1442, April.

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