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Sequencing to Minimize the Maximum Job Cost

Author

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  • Clyde L. Monma

    (Bell Laboratories, Holmdel, New Jersey)

Abstract

Consider the problem of sequencing a set of jobs in order to minimize the maximum job cost. Examples of such a problem include the one-machine maximum lateness and maximum earliness problems, the maximum cumulative cost problem, and Johnson's two-machine maximum completion time flow-shop problem. The relationships among various maximum cost problems are explored. One such result is that the first three examples cited above are special cases of the final one; even though they appear to be quite different on the surface. A consequence of this fact is that the two-machine maximum completion time flow-shop problem is NP-hard when general precedence constraints are allowed. A maximum cost problem is formulated and shown to generalize the above-mentioned problems. An extension of Lawler's back-to-front sequencing algorithm efficiently solves the unconstrained version of this problem. Finally, two insertion properties, which were motivated by Smith's adjacent pairwise interchange (API) property, lead to efficient algorithms for sequencing with general precedence constraints.

Suggested Citation

  • Clyde L. Monma, 1980. "Sequencing to Minimize the Maximum Job Cost," Operations Research, INFORMS, vol. 28(4), pages 942-951, August.
    • Handle: RePEc:inm:oropre:v:28:y:1980:i:4:p:942-951
    DOI: 10.1287/opre.28.4.942
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    Cited by:

    1. Chung-Yee Lee & Ming Liu & Chengbin Chu, 2015. "Optimal Algorithm for the General Quay Crane Double-Cycling Problem," Transportation Science, INFORMS, vol. 49(4), pages 957-967, November.
    2. A.A. Gladky & Y.M. Shafransky & V.A. Strusevich, 2004. "Flow Shop Scheduling Problems Under Machine–Dependent Precedence Constraints," Journal of Combinatorial Optimization, Springer, vol. 8(1), pages 13-28, March.
    3. Chen, Feng & Lee, Chung-Yee, 2009. "Minimizing the makespan in a two-machine cross-docking flow shop problem," European Journal of Operational Research, Elsevier, vol. 193(1), pages 59-72, February.
    4. Hans Kellerer & Vladimir Kotov & Franz Rendl & Gerhard J. Woeginger, 1998. "The Stock Size Problem," Operations Research, INFORMS, vol. 46(3-supplem), pages 1-12, June.
    5. Y.M. Shafransky & V.A. Strusevich, 1998. "The open shop scheduling problem with a given sequence of jobs on one machine," Naval Research Logistics (NRL), John Wiley & Sons, vol. 45(7), pages 705-731, October.

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