Cited By
View all- Gafarov E(2016)Graphical method to solve combinatorial optimization problemsAutomation and Remote Control10.1134/S000511791612002X77:12(2110-2117)Online publication date: 1-Dec-2016
A note on a single machine scheduling problem with generalized total tardiness objective function
Pages 72 - 76
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.
References
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Moore, J.M., An n job, one machine sequencing algorithm for minimizing the number of late jobs. Management Sci. v15 i1. 102-109.
[2]
Du, J. and Leung, J.Y.-T., Minimizing total tardiness on one processor is NP-hard. Math. Oper. Res. v15. 483-495.
[3]
Lazarev, A.A. and Gafarov, E.R., Special case of the single-machine total tardiness problem is NP-hard. J. Comput. Systems Sci. Internat. v45 i3. 450-458.
[4]
Lawler, E.L., A pseudopolynomial algorithm for sequencing jobs to minimize total tardiness. Ann. Discrete Math. v1. 331-342.
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Lazarev, A.A. and Werner, F., Algorithms for special cases of the single machine total tardiness problem and an application to the even-odd partition problem. Math. Comput. Modelling. v49 i9-10. 2061-2072.
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Lenstra, J.K., Rinnooy Kan, A.H.G. and Brucker, P., Complexity of machine scheduling problems. Ann. Discrete Math. v1. 343-362.
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Lawler, E.L. and Moore, J.M., A functional equation and its application to resource allocation and sequencing problems. Management Sci. v16. 77-84.
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Blazewicz, J., Scheduling preemptive tasks on parallel processors with information loss. Tech. Sci. Inform. v3 i6. 415-420.
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Potts, C.N. and van Wassenhove, L.N., Single machine scheduling to minimize total late work. Oper. Res. v40 i3. 586-595.
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Sterna, M., A survey of scheduling problems with late work criteria. Omega. v39 i2. 120-129.
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Lazarev, A.A. and Werner, F., A graphical realization of the dynamic programming method for solving NP-hard combinatorial problems. Comput. Math. Appl. v58 i4. 619-631.
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E.R. Gafarov, A.A. Lazarev, F. Werner, A polynomial time graphical algorithm for maximizing total tardiness on a single machine, preprint 12/10, FMA, Otto-von-Guericke-Universität Magdeburg, 2010.
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Potts, C.N. and van Wassenhove, L.N., A decomposition algorithm for the single machine total tardiness problem. Oper. Res. Lett. v1 i5. 177-181.
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- A note on a single machine scheduling problem with generalized total tardiness objective function
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Copyright © Elsevier B.V. © 2011.
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Elsevier North-Holland, Inc.
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Published: 01 January 2012
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View all- Gafarov E(2016)Graphical method to solve combinatorial optimization problemsAutomation and Remote Control10.1134/S000511791612002X77:12(2110-2117)Online publication date: 1-Dec-2016
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