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Approximation algorithms for maximizing the weighted number of early jobs on a single machine with non-availability intervals

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Abstract

In this paper we consider the maximization of the weighted number of early jobs on a single machine with non-availability constraints. We deal with the resumable and the non-resumable cases. We show that the resumable version of this problem has a fully polynomial time approximation scheme (FPTAS) even if the number of the non-availability intervals is variable and a subset of jobs has deadlines instead of due dates. For the non-resumable version we remark that the problem cannot admit an FPTAS even if all due dates are equal and only one non-availability interval occurs. Nevertheless, we show in this case that it admits a polynomial time approximation scheme (PTAS) for a constant number of non-availability intervals and arbitrary due dates.

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Acknowledgments

This work has been supported by Programme PHC AMADEUS 2012 (Project No. 25086PL).

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Authors and Affiliations

  1. LCOMS EA 7603, Université de Lorraine, Ile du Saulcy, 57000 , Metz, France

    Imed Kacem & Yann Lanuel

  2. ISOR, University of Graz, Graz, Austria

    Hans Kellerer

Authors
  1. Imed Kacem
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  2. Hans Kellerer
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  3. Yann Lanuel
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Correspondence to Imed Kacem.

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Kacem, I., Kellerer, H. & Lanuel, Y. Approximation algorithms for maximizing the weighted number of early jobs on a single machine with non-availability intervals. J Comb Optim 30, 403–412 (2015). https://doi.org/10.1007/s10878-013-9643-7

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  • DOI: https://doi.org/10.1007/s10878-013-9643-7

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