Stochastic Online Scheduling Revisited

  • Andreas S. Schulz
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5165)


We consider the problem of minimizing the total weighted completion time on identical parallel machines when jobs have stochastic processing times and may arrive over time. We give randomized as well as deterministic online and off-line algorithms that have the best known performance guarantees in either setting, deterministic and off-line or randomized and online. Our analysis is based on a novel linear programming relaxation for stochastic scheduling problems, which can be solved online.


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  1. Afrati, F., Bampis, E., Chekuri, C., Karger, D., Kenyon, C., Khanna, S., Milis, I., Queyranne, M., Skutella, M., Stein, C., Sviridenko, M.: Approximation schemes for minimizing average weighted completion time with release dates. In: Proceedings of the 40th Annual IEEE Symposium on Foundations of Computer Science, pp. 32–43 (1999)Google Scholar
  2. Borodin, A., El-Yaniv, R.: Online Computation and Competitive Analysis. Cambridge University Press, Cambridge (1998)MATHGoogle Scholar
  3. Chakrabarti, S., Phillips, C., Schulz, A., Shmoys, D., Stein, C., Wein, J.: Improved scheduling algorithms for minsum criteria. In: auf der Heide, F., Monien, B. (eds.) ICALP 1996. LNCS, vol. 1099, pp. 646–657. Springer, Heidelberg (1996)Google Scholar
  4. Chekuri, C., Motwani, R., Natarajan, B., Stein, C.: Approximation techniques for average completion time scheduling. SIAM Journal on Computing 31, 146–166 (2001)MATHCrossRefMathSciNetGoogle Scholar
  5. Chou, M., Liu, H., Queyranne, M., Simchi-Levi, D.: On the asymptotic optimality of a simple on-line algorithm for the stochastic single-machine weighted completion time problem and its extensions. Operations Research 54, 464–474 (2006)CrossRefMathSciNetMATHGoogle Scholar
  6. Chou, M., Queyranne, M., Simchi-Levi, D.: The asymptotic performance ratio of an on-line algorithm for uniform parallel machine scheduling with release dates. Mathematical Programming 106, 137–157 (2006)MATHCrossRefMathSciNetGoogle Scholar
  7. Correa, J., Wagner, M.: LP-based online scheduling: From single to parallel machines. Mathematical Programming (in press, 2008)Google Scholar
  8. Goemans, M., Queyranne, M., Schulz, A., Skutella, M., Wang, Y.: Single machine scheduling with release dates. SIAM Journal on Discrete Mathematics 15, 165–192 (2002)MATHCrossRefMathSciNetGoogle Scholar
  9. Hall, L., Schulz, A., Shmoys, D., Wein, J.: Scheduling to minimize average completion time: Off-line and on-line approximation algorithms. Mathematics of Operations Research 22, 513–544 (1997)MATHMathSciNetCrossRefGoogle Scholar
  10. Hall, W., Wellner, J.: Mean residual life. In: Csörgö, M., Dawson, D., Rao, J., Saleh, A.E. (eds.) Proceedings of the International Symposium on Statistics and Related Topics, pp. 169–184 (1981)Google Scholar
  11. Kämpke, T.: On the optimality of static priority policies in stochastic scheduling on parallel machines. Journal of Applied Probability 24, 430–448 (1987)MATHCrossRefMathSciNetGoogle Scholar
  12. Lenstra, J., Rinnooy Kan, A., Brucker, P.: Complexity of machine scheduling problems. Annals of Discrete Mathematics 1, 343–362 (1977)CrossRefMathSciNetGoogle Scholar
  13. Megow, N., Schulz, A.: On-line scheduling to minimize average completion time revisited. Operations Research Letters 32, 485–490 (2004)MATHCrossRefMathSciNetGoogle Scholar
  14. Megow, N., Uetz, M., Vredeveld, T.: Models and algorithms for stochastic online scheduling. Mathematics of Operations Research 31, 513–525 (2006)MATHCrossRefMathSciNetGoogle Scholar
  15. Megow, N., Vredeveld, T.: Approximation results for preemptive stochastic online scheduling. In: Azar, Y., Erlebach, T. (eds.) ESA 2006. LNCS, vol. 4168, pp. 516–527. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  16. Möhring, R., Radermacher, F., Weiss, G.: Stochastic scheduling problems I: General strategies. Zeitschrift für Operations Research 28, 193–260 (1984)MATHCrossRefGoogle Scholar
  17. Möhring, R., Schulz, A., Uetz, M.: Approximation in stochastic scheduling: The power of LP-based priority policies. Journal of the ACM 46, 924–942 (1999)MATHCrossRefMathSciNetGoogle Scholar
  18. Queyranne, M., Schulz, A.: Scheduling unit jobs with compatible release dates on parallel machines with nonstationary speeds. In: Balas, E., Clausen, J. (eds.) IPCO 1995. LNCS, vol. 920, pp. 307–320. Springer, Heidelberg (1995)Google Scholar
  19. Rothkopf, M.: Scheduling with random service times. Management Science 12, 703–713 (1966)MathSciNetGoogle Scholar
  20. Schulz, A., Skutella, M.: The power of α-points in preemptive single machine scheduling. Journal of Scheduling 5, 121–133 (2002a)MATHCrossRefMathSciNetGoogle Scholar
  21. Schulz, A., Skutella, M.: Scheduling unrelated machines by randomized rounding. SIAM Journal on Discrete Mathematics 15, 450–469 (2002b)MATHCrossRefMathSciNetGoogle Scholar
  22. Sgall, J.: On-line scheduling. In: Fiat, A., Woeginger, G. (eds.) Online Algorithms: The State of the Art. LNCS, vol. 1442, ch. 9, pp. 196–231. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  23. Skutella, M., Uetz, M.: Stochastic machine scheduling with precedence constraints. SIAM Journal on Computing 34, 788–802 (2005)MATHCrossRefMathSciNetGoogle Scholar
  24. Sousa, J.: Time Indexed Formulations of Non-Preemptive Single-Machine Scheduling Problems. Ph.D. thesis, Université Catholique de Louvain, Belgium (1989)Google Scholar
  25. Spencer, J.: Ten Lectures on the Probabilistic Method. CBMS-NSF Regional Conference Series in Applied Mathematics, vol. 52. SIAM, Philadelphia (1987)MATHGoogle Scholar
  26. Weber, R., Varaiya, P., Walrand, J.: Scheduling jobs with stochastically ordered processing times on parallel machines to minimize expected flowtime. Journal of Applied Probability 23, 841–847 (1986)MATHCrossRefMathSciNetGoogle Scholar
  27. Weiss, G.: Approximation results in parallel machines stochastic scheduling. Annals of Operations Research 26, 195–242 (1990)MATHCrossRefMathSciNetGoogle Scholar
  28. Weiss, G., Pinedo, M.: Scheduling tasks with exponential service times on nonidentical processors to minimize various cost functions. Journal of Applied Probability 17, 187–202 (1980)MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Andreas S. Schulz
    • 1
  1. 1.Sloan School of Management, Massachusetts Institute of Technology CambridgeUSA

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