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Parameterized Multi-Scenario Single-Machine Scheduling Problems

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Abstract

We study a class of multi-scenario single-machine scheduling problems. In this class of problems, we are given a set of scenarios with each one having a different realization of job characteristics. We consider these multi-scenario problems where the scheduling criterion can be any one of the following three: The total weighted completion time, the weighted number of tardy jobs, and the weighted number of jobs completed exactly at their due-date. As all the resulting problems are NP-hard, our analysis focuses on whether any one of the problems becomes tractable when some specific natural parameters are of limited size. The analysis includes the following parameters: The number of jobs with scenario-dependent processing times, the number of jobs with scenario-dependent weights, and the number of different due-dates.

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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, P.O.B. 653, 8410501, Beer-Sheva, Israel

    Danny Hermelin, George Manoussakis, Dvir Shabtay & Liron Yedidsion

  2. Stern School of Business, New York University, 44 West 4th Street, New York, NY, 10012, USA

    Michael Pinedo

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  1. Danny Hermelin
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  2. George Manoussakis
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  4. Dvir Shabtay
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  5. Liron Yedidsion
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Correspondence to Dvir Shabtay.

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Hermelin, D., Manoussakis, G., Pinedo, M. et al. Parameterized Multi-Scenario Single-Machine Scheduling Problems. Algorithmica 82, 2644–2667 (2020). https://doi.org/10.1007/s00453-020-00702-w

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  • DOI: https://doi.org/10.1007/s00453-020-00702-w

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