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Flow Shop Scheduling Problems Under Machine–Dependent Precedence Constraints

Author

Listed:
  • A.A. Gladky

    (Institute of Engineering Cybernetics)

  • Y.M. Shafransky

    (Institute of Engineering Cybernetics)

  • V.A. Strusevich

    (University of Greenwich)

Abstract

The paper considers the flow shop scheduling problems to minimize the makespan, provided that an individual precedence relation is specified on each machine. A fairly complete complexity classification of problems with two and three machines is obtained.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jcomop:v:8:y:2004:i:1:d:10.1023_b:joco.0000021935.66577.09
    DOI: 10.1023/B:JOCO.0000021935.66577.09
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    References listed on IDEAS

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    1. Clyde L. Monma & Jeffrey B. Sidney, 1979. "Sequencing with Series-Parallel Precedence Constraints," Mathematics of Operations Research, INFORMS, vol. 4(3), pages 215-224, August.
    2. E. L. Lawler, 1973. "Optimal Sequencing of a Single Machine Subject to Precedence Constraints," Management Science, INFORMS, vol. 19(5), pages 544-546, January.
    3. Clyde L. Monma, 1979. "The Two-Machine Maximum Flow Time Problem with Series-Parallel Precedence Constraints: An Algorithm and Extensions," Operations Research, INFORMS, vol. 27(4), pages 792-798, August.
    4. Leslie A. Hall & David B. Shmoys, 1992. "Jackson's Rule for Single-Machine Scheduling: Making a Good Heuristic Better," Mathematics of Operations Research, INFORMS, vol. 17(1), pages 22-35, February.
    5. S. M. Johnson, 1954. "Optimal two‐ and three‐stage production schedules with setup times included," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 1(1), pages 61-68, March.
    6. M. R. Garey & D. S. Johnson & Ravi Sethi, 1976. "The Complexity of Flowshop and Jobshop Scheduling," Mathematics of Operations Research, INFORMS, vol. 1(2), pages 117-129, May.
    7. 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.
    8. V.A. Strusevich, 1997. "Shop scheduling problems under precedence constraints," Annals of Operations Research, Springer, vol. 69(0), pages 351-377, January.
    9. Clyde L. Monma, 1980. "Sequencing to Minimize the Maximum Job Cost," Operations Research, INFORMS, vol. 28(4), pages 942-951, August.
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    Cited by:

    1. 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.
    2. Zhao, Chuanli & Tang, Hengyong, 2012. "Two-machine flow shop scheduling with deteriorating jobs and chain precedence constraints," International Journal of Production Economics, Elsevier, vol. 136(1), pages 131-136.

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