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A general scheme for solving a large set of scheduling problems with rejection in FPT time

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Abstract

Mnich and Wiese (Math Program 154:533–562, 2015) proved that the \(\mathcal {NP}\)-hard single-machine scheduling problem with rejection and the total weighted completion time plus total rejection cost as objective is fixed parameter tractable with respect to the number of different processing times and weights in the instance. This result is obtained by reducing the problem to an integer convex programming problem where the number of variables depends solely on the parameter (number of different processing times and weights). We show that this method can be incorporated into a more general scheme for solving a large set of scheduling problems with rejection which share common properties. These problems include various different machine environments, namely single machine, identical machines in parallel, and flow-shops.

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Acknowledgements

This research was supported by Grant No. 2016049 from the United States-Israel Binational Science Foundation (BSF).

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Authors and Affiliations

  1. Department of Industrial Engineering and Management, Ben-Gurion University of the Negev, Beer-Sheva, Israel

    Danny Hermelin, Dvir Shabtay & Chen Zelig

  2. Stern School of Business, New York University, 40 West 4th Street, New York, NY, 10012, USA

    Michael Pinedo

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  1. Danny Hermelin
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  2. Dvir Shabtay
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  3. Chen Zelig
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  4. Michael Pinedo
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Correspondence to Dvir Shabtay.

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This research was supported by Grant 2016049 of the United States-Israel Binational Science Foundation (BSF).

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Hermelin, D., Shabtay, D., Zelig, C. et al. A general scheme for solving a large set of scheduling problems with rejection in FPT time. J Sched 25, 229–255 (2022). https://doi.org/10.1007/s10951-022-00731-z

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