Optimal on-line algorithms for single-machine scheduling

  • J. A. Hoogeveen
  • A. P. A. Vestjens
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1084)


We consider single-machine on-line scheduling problems where jobs arrive over time. A set of independent jobs has to be scheduled on the machine, where preemption is not allowed and the number of jobs is unknown in advance. Each job becomes available at its release date, which is not known in advance, and its characteristics, e.g., processing requirement, become known at its arrival. We deal with two problems: minimizing total completion time and minimizing the maximum time by which all jobs have been delivered. For both problems we propose and analyze an on-line algorithm based on the following idea: As soon as the machine becomes available for processing, choose an available job with highest priority, and schedule it if its processing requirement is not too large. Otherwise, postpone the start of this job for a while. We prove that our algorithms have performance bound 2 and (√5 + 1)/2, respectively, and we show that for both problems there cannot exist an on-line algorithm with a better performance guarantee.


on-line algorithms single-machine scheduling worst-case analysis 


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  1. Chen, B., A. van Vliet, and G.J. Woeginger [1994], New lower and upper bounds for on-line scheduling, Operations Research Letters16, 221–230.MathSciNetGoogle Scholar
  2. Graham, R.L. [1966], Bounds for certain multiprocessing anomalies, Bell System Technical Journal45, 1563–1581.Google Scholar
  3. Kise, H., T. Ibaraki, and H. Mine [1979], Performance analysis of six approximation algorithms for the one-machine maximum lateness scheduling problem with ready times, Journal of the Operations Research Society of Japan22, 205–224.Google Scholar
  4. Lawler, E. L., J.K. Lenstra, A.H.G. Rinnooy Kan, and D.B. Shmoys [1993], Sequencing and scheduling: Algorithms and complexity, in: S.C. Graves, A.H.G. Rinnooy Kan, and P.H. Zipkin (eds.), Logistics of Production and Inventory, Handbooks in OR & MS 4, Elsevier Science Publishers B.V., Amsterdam, Chapter 9, 445–522, ISBN 0-444-8T472-0.Google Scholar
  5. Mao, W., R.K. Kincaid, and A. Rifkin [1995], On-line algorithms for a single machine scheduling problem, in: S.G. Nash and A. Sofer (eds.), The impact of emerging technologies on computer science and operations research, Kluwer Academic Press, Chapter 8, 157–173.Google Scholar
  6. Phillips, C., C. Stein, and J. Wein [1995], Scheduling jobs that arrive over time, Proceedings of the Fourth Workshop on Algorithms and Data Structures, Lecture Notes in Computer Science 955, Springer.Google Scholar
  7. Stougie, L. [1995], personal communication.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • J. A. Hoogeveen
    • 1
  • A. P. A. Vestjens
    • 1
  1. 1.Department of Mathematics and Computing ScienceEindhoven University of TechnologyMB, EindhovenThe Netherlands

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