Journal of Korean Institute of Industrial Engineers (대한산업공학회지)

Korean Institute of Industrial Engineers (대한산업공학회)
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Parallel Machines Scheduling with GoS Eligibility Constraints : a Survey

GoS 상황에서의 스케줄링 문제 : 문헌 조사

  • Lim, Kyung-Kuk (Department of Industrial and Management Engineering, Pohang University of Science and Technology)
  • 임경국 (포항공과대학교 산업경영공학과)
  • Received : 2010.10.18
  • Accepted : 2010.11.22
  • Published : 2010.12.01
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Abstract

In this paper, we survey the parallel machines scheduling problem with GoS eligibility constraints so as to minimize the makespan. Our survey covers off-line, online and semi-online scheduling problems. In the case of online scheduling, we only focus on online scheduling one by one. Hence we give an introduction to the problem and present important results of the problem.

Keywords

References

  1. Azar, Y., Broder, A. and Karlin, A. (1994), On-line load balancing, Theoretical Computer Science, 130, 73-84. https://doi.org/10.1016/0304-3975(94)90153-8
  2. Azar, Y., Naor, J. and Rom, R. (1995), The competitiveness of online assignments, Journal of Algorithms, 18, 221-237. https://doi.org/10.1006/jagm.1995.1008
  3. Bar-Noy, A., Freund, A., and Naor, J. (2001), Online load balancing in a hierarchical server topology, SIAM Journal on Computing, 31, 527-549. https://doi.org/10.1137/S0097539798346135
  4. Chassid, O. and Epstein, L. (2008), The hierarchical model for load balancing on two machines, Journal of Combinatorial Optimization, 15, 305-314. https://doi.org/10.1007/s10878-007-9078-0
  5. Crescenzi, P., Gambosi, G., and Penna, P. (2004), On-line algorithms for the channel assignment problem in cellular networks, Discrete Applied Mathematics, 137, 237-266. https://doi.org/10.1016/S0166-218X(03)00341-X
  6. Efraimidis, P. S. and Spirakis, P. G. (2006), Approximation schemes for scheduling and covering on unrelated machines, Theoretical Computer Science, 359, 400-417. https://doi.org/10.1016/j.tcs.2006.05.025
  7. Fishkin, A. V., Jansen, K. and Mastrolilli, M. (2008), Grouping techniques for scheduling problems : Simpler and faster, Algorithmica, 51, 183-199. https://doi.org/10.1007/s00453-007-9086-6
  8. Garey, M. R. and Johnson, D. S. (1979), Computers and intractability : A guide to the theory of NP-completeness, Freeman, New York.
  9. Glass, G. A. and Kellerer, H. (2007), Parallel machine scheduling with job assignment restrictions, Naval Research Logistics, 54, 250-257. https://doi.org/10.1002/nav.20202
  10. Horowitz, E. and Sahni, S. (1976), Exact and approximate algorithms for scheduling nonidentical processors, Journal of the Association for Computing Machinery, 23, 317-327. https://doi.org/10.1145/321941.321951
  11. Huo, Y. and Leung, J. Y.-T. (2010), Parallel machine scheduling with nested processing set restrictions, European Journal of Operational Research, 204, 229-236. https://doi.org/10.1016/j.ejor.2009.10.025
  12. Hwang, H.-C., Chang, S. Y. and Lee, K. (2004), Parallel machine scheduling under a grade of service provision, Computers and Operations Research, 31, 2055-2061. https://doi.org/10.1016/S0305-0548(03)00164-3
  13. Jansen, K. and Porkolab, L. (2001), Improved approximation schemes for scheduling unrelated parallel machines, Mathematics of Operations Research, 26, 324-338. https://doi.org/10.1287/moor.26.2.324.10559
  14. Ji, M. and Cheng, T. C. E. (2008), An FPTAS for parallel-machine scheduling under a grade of service provision to minimize makespan, Information Processing Letters, 108, 171-174. https://doi.org/10.1016/j.ipl.2008.04.021
  15. Jiang, Y. (2006), Online scheduling on parallel machines with two GoS levels, Journal of Combinatorial Optimization, 16, 28-38. Also in : Lecture Notes in Computer Science, 4041, 11-21.
  16. Jiang, Y., He, Y., and Tang, C. (2006), Optimal online algorithms for scheduling on two identical machines under a grade of service, Journal of Zhejiang University SCIENCE A, 7, 309-314.
  17. Kafura, D. G. and Shen, V. Y. (1977), Task scheduling on a multiprocessor system with independent memories, SIAM Journal of Computing, 6, 167-187. https://doi.org/10.1137/0206014
  18. Lee, K., Leung, J. Y-T., and Pinedo, M. L. (2009), Online scheduling on two uniform machines subject to eligibility constraints, Theoretical Computer Science, 410, 3975-3981. https://doi.org/10.1016/j.tcs.2009.06.032
  19. Lee, K., Leung, J. Y-T. and Pinedo, M. L. (2010), Scheduling jobs with equal processing times subject to machine eilibility constraints, Journal of Scheduling, DOI 10.1007/s10951-010-0190-0.
  20. Leung, J. Y.-T., and Li, C.-L. (2008), Scheduling with processing set restrictions : A survey, International Journal of Production Economics, 116, 251-262. https://doi.org/10.1016/j.ijpe.2008.09.003
  21. Li, C.-L. and Wang, X. (2010), Scheduling parallel machines with inclusive processing set restrictions and job release times, European Journal of Operational Research, 200, 702-710. https://doi.org/10.1016/j.ejor.2009.02.011
  22. Li, W., Li, J. and Zhang, T. (2009), Approximation schemes for scheduling on parallel machines with GoS Levels, Lecture Notes in Operations Research-Operations Research and Its Applications, 10, 53-60.
  23. Lin, Y. and Li, W. (2004), Parallel machine scheduling of machine-dependent jobs with unit-length, European Journal of Operational Research, 156, 261-266. https://doi.org/10.1016/S0377-2217(02)00914-1
  24. Lim, K., Lee, K., and Chang, Soo Y. (2010a), On optimality of a greedy approach to the online scheduling under eligibility constraints, submitted for publication.
  25. Lim, K., Chang, Soo Y., Park, J., and Lee, K. (2010b), Online and semi-online scheduling of two and three machines under a GoS provision, submitted for publication.
  26. Liu, M., Chu, C., Xu, Y., and Zheng, F. (2010), Semi-online scheduling on 2 machines under a grade of service provision with bounded processing times, Journal of Combinatorial Optimization, DOI : 10.1007/s10878-009-9231-z.
  27. Liu, M., Xu, Y., Chu, C., and Zheng, F. (2009), Online scheduling on two uniform machines to minimize the makespan, Theoretical Computer Science, 410, 2099-2109. https://doi.org/10.1016/j.tcs.2009.01.007
  28. Ou, J., Leung, J. Y.-T., and Li, C.-L. (2008), Scheduling parallel machines with inclusive processing set restrictions, Naval Research Logistics, 55, 328-338. https://doi.org/10.1002/nav.20286
  29. Park, J., Chang, Soo Y., and Lee, K. (2006), Online and semi-online scheduling of two machines under a grade of service provision, Operations Research Letters, 34, 692-696. https://doi.org/10.1016/j.orl.2005.11.004
  30. Pinedo, M. (1994), Scheduling : Theory, algorithms, and systems, New York : Prentice Hall.
  31. Tan, Z. and Zhang, A. (2009), A mathematical programming approach for online hierarchical scheduling, Lecture Notes in Computer Science, 5573, 438-450.
  32. Tan, Z. and Zhang, A. (2010a), A note on hierarchical scheduling on two uniform machines, Journal of Combinatorial Optimization, 20, 85-95. https://doi.org/10.1007/s10878-008-9195-4
  33. Tan, Z. and Zhang, A. (2010b), Online hierarchical scheduling : An approach using mathematical programming, Theoretical Computer Science, In press, Corrected Proof.
  34. Woeginger, G. J. (2009), A comment on parallel-machine scheduling under a grade of service provision to minimize makespan, Information Processing Letters, 109, 341-342. https://doi.org/10.1016/j.ipl.2008.11.008
  35. Wu, Y. and Yang, Q. (2010), Optimal semi-online scheduling algorithms on two parallel identical machines under a grade of service provision, Lecture Notes in Computer Science, 6124, 261-270.
  36. Zhang, A., Jiang, Y., and Tan, Z. (2008), Optimal algorithms for online hierarchical scheduling on parallel machines, Manuscript.
  37. Zhang, A., Jiang, Y., and Tan, Z. (2009), Online parallel machines scheduling with two hierarchies, Theoretical Computer Science, 410, 3597-3605. https://doi.org/10.1016/j.tcs.2009.04.007
  38. Zhou, P., Jiang, Y., and He, Y. (2007), Parallel machine scheduling problem with two GoS levels}, Applied Mathematics : A journal of Chinese Universities (Series A), 22, 275-284, (in Chinese).