대한산업공학회지 (Journal of Korean Institute of Industrial Engineers)

  • 제35권3호
  • /
  • Pages.213-217
  • /
  • 2009
  • /
  • 1225-0988(pISSN)
  • /
  • 2234-6457(eISSN)
대한산업공학회 (Korean Institute of Industrial Engineers)
권호 표지

작업이 일반적인 자격을 갖는 상황에서 3대의 기계와 4대의 기계의 온라인 스케줄링 문제에 대한 소고

A Note on Online Scheduling Problem of Three and Four Machines Under General Eligibility

  • 박종호 (포항공과대학교 산업경영공학부) ;
  • 장수영 (포항공과대학교 산업경영공학부) ;
  • 임경국 (포항공과대학교 산업경영공학부)
  • Park, Jong-Ho (Department of Industrial and Management Engineering, POSTECH) ;
  • Chang, Soo-Y. (Department of Industrial and Management Engineering, POSTECH) ;
  • Lim, Kyung-Kuk (Department of Industrial and Management Engineering, POSTECH)
  • 투고 : 2009.05.26
  • 심사 : 2009.06.10
  • 발행 : 2009.09.30
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

We consider the online scheduling problems of three and four machines under eligibility constraint. Respectively for the cases of three and four machines, we prove that AW algorithm has competitive ratios of $\frac{5}{2}$ and 3 which are shown to be optimal. Also, we show that the same results hold for the semi-online cases with prior knowledge of the total and the largest processing time.

키워드

참고문헌

  1. Angelelli, E., Speranza, M. G., and Tuza, Zs. (2007), Semi on-line scheduling on three processors with known sum of the tasks, Journal of Scheduling, 10, 263-269 https://doi.org/10.1007/s10951-007-0023-y
  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. Graham, R. L. (1966), Bounds for certain multiprocessor anomalies, Bell System Technical Journal, 45, 1563-1581 https://doi.org/10.1002/j.1538-7305.1966.tb01709.x
  4. He, Y. and Zhang, G. C. (1999), Semi online scheduling on two identical machines, Computing, 62, 179-187 https://doi.org/10.1007/s006070050020
  5. Hwang, H. C. Chang, S. Y., and Hong, Y. (2004), A Posterior Competitiveness for List Scheduling Algorithm on Machines with Eligibility Constraints, Asia-Pacific Journal of Operational Research, 21, 117-125 https://doi.org/10.1142/S0217595904000084
  6. Kellerer, H. Kotov, V. Speranza, M. G., and Tuza, Z. (1997), Semi-online algorithms for the partitioning problem, Operations Research Letters, 21, 235-242 https://doi.org/10.1016/S0167-6377(98)00005-4
  7. Park, J. Chang, S. 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
  8. Sleator, D. and Tarjan, R. E. (1985), Amorized efficiency of list update and paging rules, Communications of the ACM, 28, 202-208 https://doi.org/10.1145/2786.2793
  9. Tan, Z. and He, Y. (2002), Semi-online problems on two identical machines with combined partial information, Operations Research Letters, 30, 408-414 https://doi.org/10.1016/S0167-6377(02)00164-5