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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.

Suggested Citation

  • 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. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. T. C. Hu, 1961. "Parallel Sequencing and Assembly Line Problems," Operations Research, INFORMS, vol. 9(6), pages 841-848, December.
    14. 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.
    15. Clyde L. Monma, 1982. "Linear-Time Algorithms for Scheduling on Parallel Processors," Operations Research, INFORMS, vol. 30(1), pages 116-124, February.
    16. 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.
    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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    Cited by:

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    2. Jiang, Xiaojuan & Lee, Kangbok & Pinedo, Michael L., 2021. "Ideal schedules in parallel machine settings," European Journal of Operational Research, Elsevier, vol. 290(2), pages 422-434.
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    5. Zhang, An & Qi, Xiangtong & Li, Guanhua, 2020. "Machine scheduling with soft precedence constraints," European Journal of Operational Research, Elsevier, vol. 282(2), pages 491-505.
    6. Jia, Beizhen & Tierney, Kevin & Reinhardt, Line Blander & Pahl, Julia, 2022. "Optimal dual cycling operations in roll-on roll-off terminals," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 159(C).
    7. Tianyu Wang & Odile Bellenguez-Morineau, 2019. "A complexity analysis of parallel scheduling unit-time jobs with in-tree precedence constraints while minimizing the mean flow time," Journal of Scheduling, Springer, vol. 22(6), pages 709-714, December.
    8. Mina Roohnavazfar & Seyed Hamid Reza Pasandideh, 2022. "Decomposition algorithm for the multi-trip single vehicle routing problem with AND-type precedence constraints," Operational Research, Springer, vol. 22(4), pages 4253-4285, September.
    9. Luo, Kaiping & Shen, Guangya & Li, Liheng & Sun, Jianfei, 2023. "0-1 mathematical programming models for flexible process planning," European Journal of Operational Research, Elsevier, vol. 308(3), pages 1160-1175.

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