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Complexity of shop-scheduling problems with fixed number of jobs: a survey

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  • Peter Brucker
  • Yu Sotskov
  • Frank Werner

Abstract

The paper surveys the complexity results for job shop, flow shop, open shop and mixed shop scheduling problems when the number n of jobs is fixed while the number r of operations per job is not restricted. In such cases, the asymptotical complexity of scheduling algorithms depends on the number m of machines for a flow shop and an open shop problem, and on the numbers m and r for a job shop problem. It is shown that almost all shop-scheduling problems with two jobs can be solved in polynomial time for any regular criterion, while those with three jobs are NP-hard. The only exceptions are the two-job, m-machine mixed shop problem without operation preemptions (which is NP-hard for any non-trivial regular criterion) and the n-job, m-machine open shop problem with allowed operation preemptions (which is polynomially solvable for minimizing makespan). Copyright Springer-Verlag 2007

Suggested Citation

  • Peter Brucker & Yu Sotskov & Frank Werner, 2007. "Complexity of shop-scheduling problems with fixed number of jobs: a survey," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 65(3), pages 461-481, June.
    • Handle: RePEc:spr:mathme:v:65:y:2007:i:3:p:461-481
    DOI: 10.1007/s00186-006-0127-8
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    References listed on IDEAS

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    1. Sheldon B. Akers, 1956. "Letter to the Editor---A Graphical Approach to Production Scheduling Problems," Operations Research, INFORMS, vol. 4(2), pages 244-245, April.
    2. Shakhlevich, Natalia V. & Sotskov, Yuri N. & Werner, Frank, 2000. "Complexity of mixed shop scheduling problems: A survey," European Journal of Operational Research, Elsevier, vol. 120(2), pages 343-351, January.
    3. Włodzimierz Szwarc, 1960. "Solution of the Akers-Friedman Scheduling Problem," Operations Research, INFORMS, vol. 8(6), pages 782-788, December.
    4. William W. Hardgrave & George L. Nemhauser, 1963. "A Geometric Model and a Graphical Algorithm for a Sequencing Problem," Operations Research, INFORMS, vol. 11(6), pages 889-900, December.
    5. Peter Brucker & Svetlana A. Kravchenko & Yuri N. Sotskov, 1999. "Preemptive job-shop scheduling problems with a fixed number of jobs," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 49(1), pages 41-76, March.
    6. Sotskov, Yu. N., 1991. "The complexity of shop-scheduling problems with two or three jobs," European Journal of Operational Research, Elsevier, vol. 53(3), pages 326-336, August.
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    Cited by:

    1. Monaci, Marta & Agasucci, Valerio & Grani, Giorgio, 2024. "An actor-critic algorithm with policy gradients to solve the job shop scheduling problem using deep double recurrent agents," European Journal of Operational Research, Elsevier, vol. 312(3), pages 910-926.
    2. Yuri N. Sotskov & Omid Gholami, 2017. "Mixed graph model and algorithms for parallel-machine job-shop scheduling problems," International Journal of Production Research, Taylor & Francis Journals, vol. 55(6), pages 1549-1564, March.
    3. Xiong, Hegen & Fan, Huali & Jiang, Guozhang & Li, Gongfa, 2017. "A simulation-based study of dispatching rules in a dynamic job shop scheduling problem with batch release and extended technical precedence constraints," European Journal of Operational Research, Elsevier, vol. 257(1), pages 13-24.
    4. Yuri N. Sotskov, 2020. "Mixed Graph Colorings: A Historical Review," Mathematics, MDPI, vol. 8(3), pages 1-24, March.
    5. Agnetis, Alessandro & Kellerer, Hans & Nicosia, Gaia & Pacifici, Andrea, 2012. "Parallel dedicated machines scheduling with chain precedence constraints," European Journal of Operational Research, Elsevier, vol. 221(2), pages 296-305.
    6. Ahmadian, Mohammad Mahdi & Khatami, Mostafa & Salehipour, Amir & Cheng, T.C.E., 2021. "Four decades of research on the open-shop scheduling problem to minimize the makespan," European Journal of Operational Research, Elsevier, vol. 295(2), pages 399-426.
    7. Jianming Dong & Yong Chen & An Zhang & Qifan Yang, 2013. "A new three-machine shop scheduling: complexity and approximation algorithm," Journal of Combinatorial Optimization, Springer, vol. 26(4), pages 799-810, November.
    8. Gaia Nicosia & Andrea Pacifici, 2017. "Scheduling assembly tasks with caterpillar precedence constraints on dedicated machines," International Journal of Production Research, Taylor & Francis Journals, vol. 55(6), pages 1680-1691, March.

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