A note on a single machine scheduling problem with generalized total tardiness objective function

Authors:
Evgeny R. Gafarov;Alexander A. Lazarev;Frank Werner
Affiliations:
Institute of Control Sciences of the Russian Academy of Sciences, Profsoyuznaya st. 65, 117997 Moscow, Russia;Institute of Control Sciences of the Russian Academy of Sciences, Profsoyuznaya st. 65, 117997 Moscow, Russia and Lomonosov Moscow State University, Higher School of Economics, Moscow Institute of ...;Fakultät für Mathematik, Otto-von-Guericke-Universität Magdeburg, PSF 4120, 39016 Magdeburg, Germany
Venue:
Information Processing Letters
Year:
2012

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Abstract

In this note, we consider a single machine scheduling problem with generalized total tardiness objective function. A pseudo-polynomial time solution algorithm is proposed for a special case of this problem. Moreover, we present a new graphical algorithm for another special case, which corresponds to the classical problem of minimizing the weighted number of tardy jobs on a single machine. The latter algorithm improves the complexity of an existing pseudo-polynomial algorithm by Lawler. Computational results are presented for both special cases considered.