Advertisement

Journal of Zhejiang University-SCIENCE A

, Volume 8, Issue 1, pp 127–133 | Cite as

Online algorithms for scheduling with machine activation cost on two uniform machines

Article

Abstract

In this paper we investigate a variant of the scheduling problem on two uniform machines with speeds 1 and s. For this problem, we are given two potential uniform machines to process a sequence of independent jobs. Machines need to be activated before starting to process, and each machine activated incurs a fixed machine activation cost. No machines are initially activated, and when a job is revealed, the algorithm has the option to activate new machines. The objective is to minimize the sum of the makespan and the machine activation cost. We design optimal online algorithms with competitive ratio of (2s+1)/(s+1) for every s≥1.

Key words

Online algorithm Competitive analysis Uniform machine scheduling Machine activation cost 

CLC number

TP393 O223 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aspnes, J., Azar, Y., Fiat, A., Plotkin, S., Waarts, O., 1997. On-line load balancing with applications to machine scheduling and virtual circuit routing. Journal of the ACM, 44(3):486–504. [doi:10.1145/258128.258201]MathSciNetCrossRefMATHGoogle Scholar
  2. Berman, P., Charikar, M., Karpinski, M., 1997. On-line Load Balancing for Related Machines. Proceedings of the 5th Workshop on Algorithms and Data Structures. Springer-Verlag, Berlin, 1272:116–125.CrossRefGoogle Scholar
  3. Cao, D., Chen, M., Wan, G., 2005. Parallel machine selection and job scheduling to minimize machine cost and job tardiness. Computer & Operations Research, 32(8):1995–2012. [doi:10.1016/j.cor.2004.01.001]CrossRefMATHGoogle Scholar
  4. Cho, Y., Sahni, S., 1980. Bounds for list schedules on uniform processors. SIAM Journal on Computing, 9(1):91–103. [doi:10.1137/0209007]MathSciNetCrossRefMATHGoogle Scholar
  5. Dessouky, M.M., Dessouky, M.I., Verma, S., 1998. Flowshop scheduling with identical jobs and uniform parallel machines. European Journal of Operational Research, 109(3):620–631. [doi:10.1016/S0377-2217(97)00194-X]MathSciNetCrossRefMATHGoogle Scholar
  6. Dósa, G., He, Y., 2004. Better online algorithms for scheduling with machine cost. SIAM Journal on Computing, 33(5):1035–1051. [doi:10.1137/S009753970343395X]MathSciNetCrossRefMATHGoogle Scholar
  7. Epstein, L., Noga, J., Seiden, S., Sgall, J., Woeginger, G.J., 2001. Randomized on-line scheduling on two uniform machines. Journal of Scheduling, 4(2):71–92. [doi:10.1002/jos.60]MathSciNetCrossRefMATHGoogle Scholar
  8. Epstein, L., Sgall, J., 2000. A lower bound for on-line scheduling on uniformly related machines. Operations Research Letters, 26(1):17–22. [doi:10.1016/S0167-6377(99)00062-0]MathSciNetCrossRefMATHGoogle Scholar
  9. He, Y., Han, S.G., Jiang, Y.W., 2006. Online algorithms for scheduling with machine activation cost. Asia-Pacific Journal of Operations research, in press.Google Scholar
  10. Imreh, C., Noga, J., 1999. Scheduling with Machine Cost. Proc. RANDOM APPROX’99. Lecture Notes in Computer Science, 1671:168–176.MathSciNetCrossRefMATHGoogle Scholar
  11. Jiang, Y.W., He, Y., 2005. Preemptive online algorithms for scheduling with machine cost. Acta Informatica, 41(6): 315–340. [doi:10.1007/s00236-004-0156-9]MathSciNetCrossRefMATHGoogle Scholar
  12. Jiang, Y.W., He, Y., 2006. Semi-online algorithms for scheduling with machine cost. Journal of Computer Science & Technology, 21(6):984–988.MathSciNetCrossRefGoogle Scholar
  13. Noga, J., Seiden, S.S., 2001. An optimal online algorithm for scheduling two machines with release times. Theoretical Computer Science, 268(1):133–143. [doi:10.1016/S0304-3975(00)00264-4]MathSciNetCrossRefMATHGoogle Scholar
  14. Panwalkar, S., Liman, S.D., 2002. Single operation earliness-tardiness scheduling with machine activation cost. IIE Transactions, 34(5):509–513. [doi:10.1023/A:1013539825022]Google Scholar
  15. Sgall, J., 1998. On-line Scheduling. In: Fiat, A., Woeginger, G.J. (Eds.), Online Algorithms: The State of the Art. Springer-Verlag, Berlin, 1442:196–231. [doi:10.1007/BFb0029570]CrossRefGoogle Scholar
  16. Tan, Z., He, Y., 2002. Optimal online algorithm for scheduling on two identical machines with machine availability constraints. Information Processing Letters, 83(6):323–329. [doi:10.1016/S0020-0190(02)00211-9]MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  • Han Shu-guang 
    • 1
  • Jiang Yi-wei 
    • 2
  • Hu Jue-liang 
    • 2
  1. 1.Department of MathematicsZhejiang UniversityHangzhouChina
  2. 2.Faculty of ScienceZhejiang Sci-Tech UniversityHangzhouChina

Personalised recommendations