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A survey on how the structure of precedence constraints may change the complexity class of scheduling problems

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  • D. Prot

    (Ecole des Mines de Nantes)

  • O. Bellenguez-Morineau

    (Ecole des Mines de Nantes)

Abstract

This survey aims to demonstrate that the structure of precedence constraints plays a tremendous role on the complexity of scheduling problems. Indeed, many problems can be $$\mathcal {NP}$$ NP -hard when considering general precedence constraints, while they become polynomially solvable for particular precedence constraints. Additionally, the existence of many very exciting challenges in this research area is underlined.

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  • D. Prot & O. Bellenguez-Morineau, 2018. "A survey on how the structure of precedence constraints may change the complexity class of scheduling problems," Journal of Scheduling, Springer, vol. 21(1), pages 3-16, February.
    • Handle: RePEc:spr:jsched:v:21:y:2018:i:1:d:10.1007_s10951-017-0519-z
    DOI: 10.1007/s10951-017-0519-z
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    1. M.I. Dessouky & B.J. Lageweg & J.K. Lenstra & S.L. van de Velde, 1990. "Scheduling identical jobs on uniform parallel machines," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 44(3), pages 115-123, September.
    2. 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.
    3. Timkovsky, Vadim G., 2003. "Identical parallel machines vs. unit-time shops and preemptions vs. chains in scheduling complexity," European Journal of Operational Research, Elsevier, vol. 149(2), pages 355-376, September.
    4. Lushchakova, Irene N., 2006. "Two machine preemptive scheduling problem with release dates, equal processing times and precedence constraints," European Journal of Operational Research, Elsevier, vol. 171(1), pages 107-122, May.
    5. Joseph Y.-T. Leung & Gilbert H. Young, 1990. "Minimizing Total Tardiness on a Single Machine with Precedence Constraints," INFORMS Journal on Computing, INFORMS, vol. 2(4), pages 346-352, November.
    6. T. C. Hu, 1961. "Parallel Sequencing and Assembly Line Problems," Operations Research, INFORMS, vol. 9(6), pages 841-848, December.
    7. Yumei Huo & Joseph Leung, 2005. "Minimizing total completion time for UET tasks with release time and outtree precedence constraints," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 62(2), pages 275-279, November.
    8. Clyde L. Monma, 1982. "Linear-Time Algorithms for Scheduling on Parallel Processors," Operations Research, INFORMS, vol. 30(1), pages 116-124, February.
    9. Peter Brucker & Johann Hurink & Wieslaw Kubiak, 1999. "Scheduling identical jobs with chain precedence constraints on two uniform machines," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 49(2), pages 211-219, April.
    10. Lenstra, J. K. & Rinnooy Kan, A. H. G., 1980. "Complexity results for scheduling chains on a single machine," European Journal of Operational Research, Elsevier, vol. 4(4), pages 270-275, April.
    11. José R. Correa & Andreas S. Schulz, 2005. "Single-Machine Scheduling with Precedence Constraints," Mathematics of Operations Research, INFORMS, vol. 30(4), pages 1005-1021, November.
    12. Peter Brucker & M. R. Garey & D. S. Johnson, 1977. "Scheduling Equal-Length Tasks Under Treelike Precedence Constraints to Minimize Maximum Lateness," Mathematics of Operations Research, INFORMS, vol. 2(3), pages 275-284, August.
    13. Jeffrey B. Sidney, 1975. "Decomposition Algorithms for Single-Machine Sequencing with Precedence Relations and Deferral Costs," Operations Research, INFORMS, vol. 23(2), pages 283-298, April.
    14. J. K. Lenstra & A. H. G. Rinnooy Kan, 1978. "Complexity of Scheduling under Precedence Constraints," Operations Research, INFORMS, vol. 26(1), pages 22-35, February.
    15. Philippe Baptiste & Vadim G. Timkovsky, 2004. "Shortest path to nonpreemptive schedules of unit-time jobs on two identical parallel machines with minimum total completion time," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 60(1), pages 145-153, September.
    16. Djellab, Khaled, 1999. "Scheduling preemptive jobs with precedence constraints on parallel machines," European Journal of Operational Research, Elsevier, vol. 117(2), pages 355-367, September.
    17. Christoph Ambühl & Monaldo Mastrolilli & Nikolaus Mutsanas & Ola Svensson, 2011. "On the Approximability of Single-Machine Scheduling with Precedence Constraints," Mathematics of Operations Research, INFORMS, vol. 36(4), pages 653-669, November.
    18. Martin Middendorf & Vadim G. Timkovsky, 1999. "Transversal Graphs for Partially Ordered Sets: Sequencing, Merging and Scheduling Problems," Journal of Combinatorial Optimization, Springer, vol. 3(4), pages 417-435, December.
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