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Open shop scheduling with some additional constraints


An open shop scheduling problem is presented; preemptions during processing of a job on a processorp is allowed but the job cannot be sent on another processorq before it is finished onp. A graph-theoretical model is described and a characterization is given for problems where schedules with such restricted preemptions useT time units whereT is the maximum of the processing times of the jobs and of the working times of the processors. The general case is shown to be NP-complete. We also consider the case where some constraints of simultaneity are present. Complexity of the problem is discussed and a solvable case is described.

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  1. 1.

    Agnetis, A., Lucertini, M., Nicolo, F.: Modelling and Optimizaion of a Flexible Pipeline Assembling System. Report 04.89 Dept of Computer and System Science, University of Roma “La Sapienza”

  2. 2.

    Berge, C.: Graphes, Gauthier-Villars, Paris, 1983

  3. 3.

    Blazewicz, J., Cellary, W., Slowinski, R., Weglarz, J.: Scheduling under Resource Constraints-Deterministic Models. Annals of Operations Research (Balzer AG, Basel, 1986)

  4. 4.

    Even, S., Itai, A., Shamir, A.: On the complexity of timetable and multicommodity flow problems, SIAM Journal on Computing5, 691–703 (1976)

  5. 5.

    Gonzales, T., Sahni, S.: Open shop scheduling to minimize finish time. Journal of ACM23, 665–679 (1976)

  6. 6.

    Mahadev, N.V.R., Solot, Ph., de Werra, D.: Cylindrical Open Shop Scheduling: Some Solvable Cases, Vishwa International Journal of Graph Theory1, 29–52 (1992)

  7. 7.

    Trotter, L.E.: Line-perfect graphs. Mathematical Programming12, 255–259 (1977)

  8. 8.

    de Werra, D., Solot, Ph.: Compact cylindrical chromatic scheduling. SIAM Journal on Discrete Mathematics4, 528–534 (1991)

  9. 9.

    de Werra, D.: Graph-Theoretical Models for Preemptive Scheduling in: Advances in Project Scheduling, R. Slowinski, J. Weglarz, eds. (Elsevier Science Publishers, Amsterdam, 1989), 171–185

  10. 10.

    de Werra, D.: Almost nonpreemptive schedules. Annals of Operations Research26, 243–256 (1990)

  11. 11.

    de Werra, D., Mahadev, N.V.R., Peled, U.: Edge chromatic scheduling with simultaneity constraints. SIAM Journal on Discrete Math.6, 631–641 (1993)

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de Werra, D., Erschler, J. Open shop scheduling with some additional constraints. Graphs and Combinatorics 12, 81–93 (1996).

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  • Open shop scheduling
  • preemptions
  • line-perfectness
  • unrelated processors
  • chromatic scheduling
  • simultaneity