Journal of Scheduling

, Volume 14, Issue 1, pp 27–38 | Cite as

Scheduling jobs with equal processing times subject to machine eligibility constraints

  • Kangbok Lee
  • Joseph Y.-T. Leung
  • Michael L. Pinedo
Article

Abstract

We consider the problem of nonpreemptively scheduling a set of n jobs with equal processing times on m parallel machines so as to minimize the makespan. Each job has a prespecified set of machines on which it can be processed, called its eligible set. We consider the most general case of machine eligibility constraints as well as special cases of nested and inclusive eligible sets. Both online and offline models are considered. For offline problems we develop optimal algorithms that run in polynomial time, while for online problems we focus on the development of optimal algorithms of a new and more elaborate structure as well as approximation algorithms with good competitive ratios.

Keywords

Parallel machine scheduling Eligibility constraint Nested and inclusive eligible sets Equal-processing-time jobs Online and offline scheduling Makespan Competitive ratio Worst-case ratio 

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References

  1. Azar, Y., Naor, J., & Rom, R. (1995). The competitiveness of on-line assignments. Journal of Algorithms, 18, 221–237. CrossRefGoogle Scholar
  2. Bar-Noy, A., Freund, A., & Naor, J. (2001). Online load balancing in a hierarchical server topology. SIAM Journal of Computing, 31, 527–549. CrossRefGoogle Scholar
  3. Brucker, P., Jurisch, B., & Kramer, A. (1997). Complexity of scheduling problems with multi-purpose machines. Annals of Operations Research, 70, 57–73. CrossRefGoogle Scholar
  4. Brucker, P., & Kravchenko, S. A. (2008). Scheduling jobs with equal processing times and time windows on identical parallel machines. Journal of Scheduling, 11, 229–237. CrossRefGoogle Scholar
  5. Centeno, G., & Armacost, R. L. (2004). Minimizing makespan on parallel machines with release time and machine eligibility restrictions. International Journal of Production Research, 42, 1243–1256. CrossRefGoogle Scholar
  6. Chen, B., Potts, C. N., & Woeginger, G. J. (1998). In D.-Z. Du & P. M. Pardalos (Eds.), Handbook of combinatorial optimization : Vol. 3. A review of machine scheduling: complexity, algorithms and approximability (pp. 21–169). Boston: Kluwer Academic. Google Scholar
  7. Garey, M. R., & Johnson, D. S. (1978). Strong NP-completeness results: Motivation, examples, and implications. Journal of the Association for Computing Machinery, 25, 499–508. Google Scholar
  8. Glass, C. A., & Kellerer, H. (2007). Parallel machine scheduling with job assignment restrictions. Naval Research Logistics, 54, 250–257. CrossRefGoogle Scholar
  9. Glass, C. A., & Mills, H. R. (2006). Scheduling unit length jobs with parallel nested machine processing set restrictions. Computers & Operations Research, 33, 620–638. CrossRefGoogle Scholar
  10. Hopcroft, J. E., & Karp, R. M. (1973). An O(n 5/2) algorithm for maximum matchings in bipartite graphs. SIAM Journal of Computing, 2, 225–231. CrossRefGoogle Scholar
  11. Huo, Y., & Leung, J. Y.-T. (2010). Parallel machine scheduling with nested processing set restrictions. European Journal of Operational Research, 204, 229–236. CrossRefGoogle Scholar
  12. Hwang, H.-C., Chang, S. Y., & Lee, K. (2004). Parallel machine scheduling under a grade of service provision. Computers & Operations Research, 31, 2055–2061. CrossRefGoogle Scholar
  13. Kravchenko, S. A., & Werner, F. (2009). On a parallel machine scheduling problem with equal processing times. Discrete Applied Mathematics, 157, 848–852. CrossRefGoogle Scholar
  14. Lenstra, J. K., Shmoys, D. B., & Tardos, E. (1990). Approximation algorithms for scheduling unrelated parallel machines. Mathematical Programming, 46, 259–271. CrossRefGoogle Scholar
  15. Leung, J. Y.-T., & Li, C.-L. (2008). Scheduling with processing set restrictions: a survey. International Journal of Production Economics, 116, 251–262. Google Scholar
  16. Lin, Y., & Li, W. (2004). Parallel machine scheduling of machine-dependent jobs with unit-length. European Journal of Operational Research, 156, 261–266. CrossRefGoogle Scholar
  17. Li, C.-L. (2006). Scheduling unit-length jobs with machine eligibility restrictions. European Journal of Operational Research, 174, 1325–1328. CrossRefGoogle Scholar
  18. Ou, J., Leung, J. Y.-T., & Li, C.-L. (2008). Scheduling parallel machines with inclusive processing set restrictions. Naval Research Logistics, 55, 328–338. CrossRefGoogle Scholar
  19. Pinedo, M. L. (1995). Scheduling—theory, algorithms and systems. New York: Prentice Hall. Google Scholar
  20. Shchepin, E. V., & Vakhania, N. (2005). An optima rounding gives a better approximation for scheduling unrelated machines. Operations Research Letters, 33, 127–133. CrossRefGoogle Scholar
  21. Simons, B. (1983). Multiprocessor scheduling of unit-time jobs with arbitrary release times and deadlines. SIAM Journal of Computing, 12, 294–299. CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Kangbok Lee
    • 1
  • Joseph Y.-T. Leung
    • 2
  • Michael L. Pinedo
    • 1
  1. 1.Department of Information, Operations & Management Sciences, Stern School of BusinessNew York UniversityNew YorkUSA
  2. 2.Department of Computer ScienceNew Jersey Institute of TechnologyNewarkUSA

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