Abstract
In this paper, we consider some scheduling problems on a single machine, where weighted or unweighted total tardiness has to be maximized in contrast to usual minimization problems. These problems are theoretically important and have also practical interpretations. For the total weighted tardiness maximization problem, we present an NP-hardness proof and a pseudo-polynomial solution algorithm. For the unweighted total tardiness maximization problem with release dates, NP-hardness is proven. Complexity results for some other classical objective functions (e.g., the number of tardy jobs, total completion time) and various additional constraints (e.g., deadlines, weights and/or release dates of jobs may be given) are presented as well.
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Acknowledgements
This work has been partially supported by DAAD (Deutscher Akademischer Austauschdienst): A/08/80442/Ref. 325 and by RFBR (Russian Foundation for Basic Research): 11-08-13121. The authors are grateful to the anonymous referees for their constructive suggestions which helped us to improve the presentation.
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Gafarov, E.R., Lazarev, A.A. & Werner, F. Single machine total tardiness maximization problems: complexity and algorithms. Ann Oper Res 207, 121–136 (2013). https://doi.org/10.1007/s10479-012-1288-x
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DOI: https://doi.org/10.1007/s10479-012-1288-x