Asymptotic performance ratio of an online algorithm for the single machine scheduling with release dates

IEEE Transactions on Automatic Control

Volumn 49, Issue 5, 2004, Pages 772-776

  Chou, Cheng Feng Mabel ^a,b  

^a NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

^b SINGAPORE MIT ALLIANCE   (Singapore)

Author keywords

Algorithms; Mathematical programming; Scheduling

Indexed keywords

ALGORITHMS; JOB ANALYSIS; LINEAR PROGRAMMING; PROBABILITY; SCHEDULING; THEOREM PROVING;

ONLINE ALGORITHM; RELEASE DATES; SINGLE MACHINE SCHEDULING;

ASYMPTOTIC STABILITY;

EID: 2942617196     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2004.825984     Document Type: Article

References (16)

1. W. Smith, "Various optimizers for single-stage production," Naval Res. Log. Quart., vol. 3, pp. 59-66, 1956.
2. J. K. Lenstra, A. H. G. R. Kan, and P. Brucker, "Complexity of machine scheduling problems," Ann. Discrete Math., vol. 1, pp. 343-362, 1977.
3. C. Phillips, C. Stein, and J. Wein, "Minimizing average completion time in the presence of release dates," Math. Program., vol. 82, pp. 199-223, 1998.
4. J. A. Hoogeveen and A. P. A. Vestjens, "Optimal online algorithms for single-machine scheduling," in Proc. 5th Conf. Integer Programming Combinatorial Optimization, 1996, pp. 404-414.
5. C. Chekuri, R. Motwani, B. Natarajan, and C. Stein, "Approximation techniques for average completion time scheduling," in Proc. 8th Annu. ACM-SIAM Symp. Discrete Algorithms, 1997, pp. 609-618.
6. L. A. Hall, A. S. Schulz, D. B. Shmoys, and J. Wein, "Scheduling to minimize average completion time: Offline and online approximation algorithms," Math. Oper. Res., vol. 22, no. 3, pp. 513-544, 1997.
7. S. Chakrabarti, C. Phillips, A. Shmoys, C. Stein, and J. Wein, Improved Algorithms for Minsum Criteria, ser. Lecture Notes in Computer Science. New York: Springer-Verlag, 1996, pp. 646-657.
8. M. X. Goemans, "Improved approximation algorithms for scheduling with release dates," in Proc. 8th ACM-SIAM Symp. Discrete Algorithms, 1997, pp. 591-598.
9. M. X. Goemans, M. Queyranne, A. S. Schulz, M. Skutella, and Y. Wang, "Single machine scheduling with release dates," SIAM J. Discrete Math., vol. 15, pp. 165-192, 2002.
10. P. Kaminsky and D. Simchi-Levi, "Probabilistic analysis of an online algorithm for the single machine mean completion time problem with release dates," Oper. Res. Lett., vol. 21, pp. 141-148, 2001.
11. L. Schrage, "A proof of the optimality of the shortest remaining processing time discipline," Oper. Res., vol. 16, pp. 687-690, 1968.
12. J. Labetoulle, E. L. Lawler, J. K. Lenstra, and A. H. G. R. Kan, "Preemptive scheduling of uniform machines subject to release dates," in Progress in Combinatorial Optimization, W. Pulleyblank, Ed. New York: Academic, 1984, pp. 245-261.
13. M. E. Dyer and L. A. Wolsey, "Formulating the single machine sequencing problem with release dates as a mixed integer program," Discrete Appl. Math., vol. 26, pp. 255-270, 1990.
14. R. N. Uma and J. Wein, On the Relationship Between Combinatorial and LP-Based Approaches to NP-Hard Scheduling Problems, ser. Lecture Notes in Computer Science. New York: Springer-Verlag, 1998, pp. 394-408.
15. H. Liu, "Probabilistic analysis and practical algorithms for machine scheduling problems with or without release dates constraints," Ph.D. dissertation, Northwestern Univ., Evanston, IL, 2001.
16. C. M. Chou, M. Queyranne, and D. Simchi-Levi, "The asymptotic performance ration of an on-line algorithm for uniform parallel machine scheduling with release dates," in Proc. 8th Conf. Integer Programming Combinatorial Optimization, 2001, pp. 45-59.