On-Line Algorithms for a Single Machine Scheduling Problem

  • Weizhen Mao
  • Rex K. Kincaid
  • Adam Rifkin
Part of the Operations Research/Computer Science Interfaces Series book series (ORCS, volume 4)


An increasingly significant branch of computer science is the study of on-line algorithms. In this paper, we apply the theory of on-line algorithms to job scheduling. In particular, we study the nonpreemptive single machine scheduling of independent jobs with arbitrary release dates to minimize the total completion time. We design and analyze two on-line algorithms which make scheduling decisions without knowing about jobs that will arrive in future.


Schedule Problem Completion Time Tabu Search Optimal Schedule Competitive Ratio 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    S. Chand, R. Traub, and R. Uzsoy, 1993. Single machine scheduling with dynamic arrivals:Decomposition results and a forward algorithm, technical Report 93-10, School of Industrial Engineering, Purdue University, West Lafayette, IN.Google Scholar
  2. [2]
    C. Chu, 1992. Efficient heuristics to minimize total flow time with release dates, Oper. Res. Lett. IS, 321–330.Google Scholar
  3. [3]
    R. W. Conway, W. L. Maxwell, and L. W. Miller, 1967. Theory of Schedul ing, Addison-Wesley, Reading, MA.Google Scholar
  4. [4]
    J. S. Deogun, 1983. On scheduling with ready times to minimize mean flow time, Comput. J. 26, 320–328.Google Scholar
  5. [5]
    M. I. Dessouky and J. S. Deogun, 1981. Sequencing jobs with unequal ready times to minimize mean flow time, SIAM J. Comput. 10, 192–202.CrossRefGoogle Scholar
  6. [6]
    P. G. Gazmuri, 1985. Probabilistic analysis of a machine scheduling prob lem, Math. Oper. Res. 10, 328–339.CrossRefGoogle Scholar
  7. [7]
    F. Glover, 1990. Tabu Search:A Tutorial, Interfaces 20, 74–94.Google Scholar
  8. [8]
    F. Glover and M. Laguna, 1993. Tabu Search in Modern Heuristic Tech niques for Combinatorial Problems, C. R. Reeves, ed., Blackwell Scientific Publishing, 70–150.Google Scholar
  9. [9]
    R. L. Graham, 1969. Bounds on multiprocessing timing anomalies, SIAM J. Appl. Math. 17, 416–429.CrossRefGoogle Scholar
  10. [10]
    D. Gross and C. M. Harris, 1974. Fundamentals of Queuemg Theory, John Wiley and Sons, New York.Google Scholar
  11. [11]
    L. Hall and D. Shmoys, 1992. Jackson’s Rule for One-Machine Scheduling:Making a Good Heuristic Better, Math. Oper. Res. 17, 22–35.CrossRefGoogle Scholar
  12. [12]
    A. R. Karlin, M. S. Manasse, L. Rudolph, and D. D. Sleator, 1988. Com petitive snoopy caching, Algorithmica 3, 79–119.CrossRefGoogle Scholar
  13. [13]
    R. M. Karp, 1992. On-line Algorithms Versus Off-line Algorithms:How Much is it Worth to Know the Future?, International Computer Science Institute Technical Report TR-92-044, Berkeley, CA.Google Scholar
  14. [14]
    R. Kincaid, 1992. Good Solutions to Discrete Noxious Location Problems, Ann. of Oper. Res. 40, 265–281.CrossRefGoogle Scholar
  15. [15]
    E. L. Lawler, J. K. Lenstra, A. H. G. Rinnooy Kan and D. B. Shmoys, 1990. Sequencing and Scheduling:Algorithms and Complexity, in Handbooks in Operations Research and Management Science, Volume 4-Logistics of Production and Inventory, S. C. Graves, A. H. G. Rinnooy Kan and P. Zipkin, ed., North-Holland.Google Scholar
  16. [16]
    J. K. Lenstra, A. H. G. Rinnooy Kan and P. Brucker, 1977. Complexity of Machine Scheduling Problems, Ann. Discrete Math. 1, 343–362.Google Scholar
  17. [17]
    M. S. Manasse, L. A. McGeoch and D. D. Sleator, 1990. Competitive Algorithms for Server Problems, J. of Algorithms 11, 208–230.Google Scholar
  18. [18]
    T. E. Phipps, 1956. Machine Repair as a Priority Waiting-line Problem, Oper. Res. 4, 45–61.CrossRefGoogle Scholar
  19. [19]
    M. E. Posner, 1988. The Deadline Constrained Weighted Completion Time Problem:Analysis of a Heuristic, Oper. Res. 36, 742–746.Google Scholar
  20. [20]
    C. N. Potts, 1980. Analysis of a Heuristic for One Machine Sequencing with Release Dates and Delivery Times, Oper. Res. 28, 1436–1441.Google Scholar
  21. [21]
    A. A. B. Pritsker, 1986. An Introduction to Simulation and SLAM II, John Wiley and Sons, New York.Google Scholar
  22. [22]
    L. Schräge, 1969. A Proof of the Optimality of the Shortest Remaining Service Time Discipline, Oper. Res. 16, 687–690.Google Scholar
  23. [23]
    J. Skorin-Kapov, 1990. Tabu Search Applied to the Quadratic Assignment Problem, ORSA J. on Comput. 2, 33-a-45.Google Scholar
  24. [24]
    D. D. Sleator and R. E. Tarjan, 1985. Amortized Efficiency of List Update and Paging Rules, Comm. A CM 28, 202–208.Google Scholar
  25. [25]
    W. E. Smith, 1956. Various Optimizers for Single-Stage Production, Naval Res. Logist. Quart. 3, 56–66.Google Scholar

Copyright information

© Springer Science+Business Media New York 1995

Authors and Affiliations

  • Weizhen Mao
    • 1
  • Rex K. Kincaid
    • 2
  • Adam Rifkin
    • 3
  1. 1.Department of Computer ScienceCollege of William and MaryWilliamsburgUSA
  2. 2.Department of MathematicsCollege of William and MaryWilliamsburgUSA
  3. 3.Department of Computer ScienceCalifornia Institute of TechnologyPasadenaUSA

Personalised recommendations