Encyclopedia of Algorithms

2008 Edition
| Editors: Ming-Yang Kao

Minimum Makespan on Unrelated Machines

1990; Lenstra, Shmoys, Tardos
  • Maxim Sviridenko
Reference work entry
DOI: https://doi.org/10.1007/978-0-387-30162-4_238

Keywords and Synonyms

Schedule of minimum length on different machines      

Problem Definition

Consider the following scheduling problem. There are m parallel machines and n independent jobs. Each job is to be assigned to one of the machines. The processing of job j on machine i requires \( p_{ij} \)

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Recommended Reading

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    Jeng-Fung, C.: Unrelated parallel machine scheduling with secondary resource constraints. Int. J. Adv. Manuf. Technol. 26, 285–292 (2005)Google Scholar
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    Grigoriev, A., Sviridenko, M., Uetz, M.: Machine scheduling with resource dependent processing times. Math. Program. 110(1B), 209–228 (2002)MathSciNetGoogle Scholar
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    Hochbaum, D.S., Shmoys, D.B.: Using dual approximation algorithms for scheduling problems: theoretical and practical results. J. Assoc. Comput. Mach. 34(1), 144–162 (1987)MathSciNetGoogle Scholar
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    Hochbaum, D.S., Shmoys, D.B.: A polynomial approximation scheme for scheduling on uniform processors: using the dual approximation approach. SIAM J. Comput. 17(3), 539–551 (1988)MathSciNetMATHGoogle Scholar
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    Lawler, E.L., Lenstra, J.K., Rinnooy Kan, A.H.G., Shmoys, D.B.: Sequencing and Scheduling: Algorithms and Complexity. In: Graves, S.C., Rinnooy Kan, A.H.G., Zipkin, P.H. (eds.) Logistics of Production and Inventory. Handbooks in Operations Research and Management Science, vol. 4, pp. 445–522. North–Holland, Amsterdam (1993)Google Scholar
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    Lenstra, J.K., Shmoys, D., Tardos, E.: Approximation algorithms for scheduling unrelated parallel machines. Math. Program. 46(3A), 259–271 (1990)MathSciNetMATHGoogle Scholar
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    Shmoys, D., Tardos, E.: An approximation algorithm for the generalized assignment problem. Math. Program. 62(3A), 461–474 (1993) MathSciNetGoogle Scholar
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    Yu, L., Shih, H., Pfund, M., Carlyle, W., Fowler, J.: Scheduling of unrelated parallel machines: an application to PWB manufacturing. IIE Trans. 34, 921–931 (2002)Google Scholar

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  • Maxim Sviridenko
    • 1
  1. 1.IBM ResearchIBMYorktown HeightsUSA