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Single machine scheduling with forbidden start times

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Abstract

This paper addresses a single machine scheduling problem in which the following simple constraint is added: a set of time slots is forbidden for starting a task, that is no task can start at any forbidden time point. We show that the single machine problem with makespan minimization is strongly \(\mathcal {NP}\) -complete and we give polynomial algorithms to solve the problems with a small number of forbidden start times.

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Authors and Affiliations

  1. Laboratoire d’Informatique, Université François-Rabelais de Tours, 64 avenue Jean Portalis, 37200, Tours, France

    Jean-Charles Billaut

  2. LIP6, CNRS, Université Pierre et Marie Curie, 4 place Jussieu, 75252, Paris cedex 05, France

    Francis Sourd

Authors
  1. Jean-Charles Billaut
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  2. Francis Sourd
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Correspondence to Francis Sourd.

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Billaut, JC., Sourd, F. Single machine scheduling with forbidden start times. 4OR-Q J Oper Res 7, 37–50 (2009). https://doi.org/10.1007/s10288-007-0061-5

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  • DOI: https://doi.org/10.1007/s10288-007-0061-5

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