Journal of Scheduling

, Volume 19, Issue 5, pp 609–616 | Cite as

High-multiplicity scheduling on one machine with forbidden start and completion times

  • Michaël Gabay
  • Christophe Rapine
  • Nadia Brauner


We are interested in a single machine scheduling problem where jobs can neither start nor end on some specified instants, and the aim is to minimize the makespan. This problem models the situation where an additional resource, subject to unavailability constraints, is required to start and to finish a job. We consider in this paper the high-multiplicity version of the problem, when the input is given using a compact encoding. We present a polynomial time algorithm for large diversity instances (when the number of different processing times is greater than the number of forbidden instants). We also show that this problem is fixed-parameter tractable when the number of forbidden instants is fixed, regardless of jobs characteristics.


Scheduling High-multiplicity Availability constraints Parameterized complexity 



This work has been partially supported by the LabEx PERSYVAL-Lab (ANR—11-LABX-0025).


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Michaël Gabay
    • 1
    • 2
  • Christophe Rapine
    • 3
  • Nadia Brauner
    • 1
    • 2
  1. 1.Université Grenoble Alpes, G-SCOPGrenobleFrance
  2. 2.CNRS, G-SCOPGrenobleFrance
  3. 3.Université de Lorraine, Laboratoire LGIPM, Ile du SaulcyMetzFrance

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