Abstract
In this paper, we consider the semi-online hierarchical scheduling for load balancing on two identical machines. In the problem, the jobs are available online over list and the objective is to minimize the \(l_p\)-norm of the two machines’ loads. Two semi-online versions are investigated: the buffer version and the rearrangement version. We design a unified optimal semi-online algorithm for both models.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Avidor A, Azar Y, Sgall J (2001) Ancient and new algorithms for load balancing in the \(l_p\) norm. Algorithmica 29:422–441
Bar-Noy A, Freund A, Naor J (2001) Online load balancing in a hierarchical server topology. SIAM J Comput 31:527–549
Chandra AK, Wong CK (1975) Worst-case analysis of a placement algorithm related to storage allocation. SIAM J Comput 4:249–263
Chen X, Xu ZZ, Dósa G, Han X, Jiang H (2013) Semi-online hierarchical scheduling problems with buffer or rearrangements. Inf Process Lett 113:127–131
Graham RL, Lawler EL, Lenstra JK, Rinnooy Kan AHG (1979) Optimization and approximation in deterministic sequencing and scheduling: a survey. Ann Discrete Math 5:287–326
Hwang HC, Chang SY, Lee K (2004) Parallel machine scheduling under a grade of service provision. Comput Oper Res 31:2055–2061
Jiang YW, He Y, Tang CM (2006) Optimal online algorithms for scheduling on two identical machines under a grade of service. J Zhejiang Univ Sci 7A:309–314
Kellerer H, Kotov V, Speranza MG, Tuza Z (1997) Semi on-line algorithms for the partition problem. Oper Res Lett 21:235–242
Lee K, Leung JY-T, Pinedo ML (2013) Makespan minimization in online scheduling with machine eligibility. Ann Oper Res 204:189–222
Leung JY-T, Li C-L (2008) Scheduling with processing set restrictions: a survey. Int J Prod Econ 116:251–262
Liu M, Chu CB, Xu YF, Zheng FF (2011) Semi-online scheduling on two machines under a grade of service provision with bounded processing times. J Comb Optim 21:138–149
Luo TB, Xu YF, Luo L, He CZ (2014) Semi-online scheduling with two GoS levels and unit processing time. Theor Comput Sci 521:62–72
Park J, Chang SY, Lee K (2006) Online and semi-online scheduling of two machines under a grade of service provision. Oper Res Lett 34:692–696
Qi XL, Yuan JJ (2016) Online and semi-online hierarchical scheduling for \(l_p\)-norm load balancing on two identical machines (submitted)
Tan ZY, Zhang A (2011) Online hierarchical scheduling: an approach using mathematical programming. Theor Comput Sci 412:246–256
Wu Y, Ji M, Yang Q (2012) Optimal semi-online scheduling algorithms on two parallel identical machines under a grade of service provision. Int J Prod Econ 135:367–371
Zhang A (2009) A study of online hierarchical scheduling and some related problems. Ph.D thesis, Zhejiang University
Zhang A, Jiang YW, Fan LD, Hu JL (2015) Optimal online algorithms on two hierarchical machines with tightly-grouped processing times. J Comb Optim 29:781–795
Acknowledgements
The authors would like to thank the associate editor and two anonymous referees for their constructive comments and kind suggestions. This research was financially supported by NSFC(11671368) and NSF-Henan(15IRTSTHN006).
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that there is no conflict of interests regarding the publication of this paper.
Rights and permissions
About this article
Cite this article
Qi, X., Yuan, J. Semi-online hierarchical scheduling for \(l_p\)-norm load balancing with buffer or rearrangements. 4OR-Q J Oper Res 15, 265–276 (2017). https://doi.org/10.1007/s10288-016-0334-y
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10288-016-0334-y