Abstract
We consider online scheduling with restarts in an unbounded parallel-batch processing system to minimize the makespan. By online we mean that jobs arrive over time and all the information on a job is unknown before its arrival time (release date) and restart means that a running batch may be interrupted, losing all the work done on it, and the jobs in the interrupted batch are released and become independently unscheduled jobs. It is known in the literature that the considered problem has no online algorithm with a competitive ratio less than \((5-\sqrt{5})/2\). We give an online algorithm for the considered problem with a competitive ratio \((5-\sqrt{5})/2\approx 1.382\).
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Brucker, P., Gladky, A., Hoogeveen, H., Kovalyov, M. Y., Potts, C. N., Tautenhahn, T., & van de Velde, S. L. (1998). Scheduling a batching machine. Journal of Scheduling, 1, 31–54.
Deng, X. T., Poon, C. K., & Zhang, Y. (2003). Approximation algorithms in batch processing. Journal of Combinatorial Optimization, 7, 247–257.
Epstein, L., & Stee, R. V. (2003). Lower bounds for on-line single-machine scheduling. Theoretical Computer Science, 299, 439–450.
Fu, R. Y., Tian, J., Yuan, J. J., & Lin, Y. X. (2007). On-line scheduling in a parallel batch processing system to minimize makespan using restarts. Theoretical Computer Science, 374, 196–202.
Fu, R. Y., Tian, J., Yuan, J. J., & He, C. (2008). On-line scheduling on a batch machine to minimize makespan with limited restarts. Operations Research Letters, 36, 255–258.
Hoogeveen, H., Potts, C. N., & Woeginger, G. J. (2000). On-line scheduling on a single machine: Maximizing the number of early jobs. Operations Research Letters, 27, 193–197.
Lagoudis, I. N., Fragkos, S. N., & Litinas, N. A. (2010). Estimating optimum container and vessel fleet sizes in a cyclic liner service using a holistic approach. International Journal of Shipping and Transport Logistics, 2, 4–21.
Lee, C. Y., & Uzsoy, R. (1999). Minimizing makespan on a single batch processing machine with dynamic job arrivals. International Journal of Production Research, 37, 219–236.
Poon, C. K., & Yu, W. C. (2005). On-line scheduling algorithms for a batch machine with finite capacity. Journal of Combinatorial Optimization, 9, 167–186.
Song, D. P., Dong, J. X., & Roe, M. (2010). Optimal container dispatching policy and its structure in a shuttle service with finite capacity and random demands. International Journal of Shipping and Transport Logistics, 2, 44–58.
Stee, R. V., & Poutre, H. L. (2005). Minimizing the total completion time on-line on a single machine, using restarts. Journal of Algorithms, 57, 95–129.
van den Akker, M., Hoogeveen, H., & Vakhania, N. (2000). Restarts can help in the on-line minimization of the maximum delivery time on a single machine. Journal of Scheduling, 3, 333–341.
Zhang, G., Cai, X., & Wong, C. K. (2001). On-line algorithms for minimizing makespan on batch processing machines. Naval Research Logistics, 48, 241–258.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Yuan, J., Fu, R., Ng, C.T. et al. A best online algorithm for unbounded parallel-batch scheduling with restarts to minimize makespan. J Sched 14, 361–369 (2011). https://doi.org/10.1007/s10951-010-0172-2
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10951-010-0172-2