Abstract
In this paper, we consider two scheduling problems on a single machine, where a specific objective function has to be maximized in contrast to usual minimization problems. We propose exact algorithms for the single machine problem of maximizing total tardiness 1‖max-ΣT j and for the problem of maximizing the number of tardy jobs 1‖maxΣU j . In both cases, it is assumed that the processing of the first job starts at time zero and there is no idle time between the jobs. We show that problem 1‖max-ΣT j is polynomially solvable. For several special cases of problem 1‖maxΣT j , we present exact polynomial algorithms. Moreover, we give an exact pseudo-polynomial algorithm for the general case of the latter problem and an alternative exact algorithm.
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Original Russian Text © E.R. Gafarov, A.A. Lazarev, F. Werner, 2010, published in Avtomatika i Telemekhanika, 2010, No. 10, pp. 63–79.
This work was supported by DAAD (Deutscher Akademischer Austauschdienst), project no. A/08/80442/Ref. 325 and the Presidium of the Russian Academy of Sciences, programs nos. 15 and 29.
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Gafarov, E.R., Lazarev, A.A. & Werner, F. Algorithms for some maximization scheduling problems on a single machine. Autom Remote Control 71, 2070–2084 (2010). https://doi.org/10.1134/S0005117910100061
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DOI: https://doi.org/10.1134/S0005117910100061