[go: up one dir, main page]
More Web Proxy on the site http://driver.im/ Skip to main content
Springer Nature Link
Log in

Makespan minimization in online scheduling with machine eligibility

  • Published:
Annals of Operations Research Aims and scope Submit manuscript

Abstract

In this paper we provide a survey of online scheduling in parallel machine environments with machine eligibility constraints and the makespan as objective function. We first give a brief overview of the different parallel machine environments and then survey the various types of machine eligibility constraints, including tree-hierarchical processing sets, Grade of Service processing sets, interval processing sets, and nested processing sets. We furthermore describe the relationships between the various different types of processing sets. We proceed with describing two basic online scheduling paradigms, namely online over list and online over time. For each one of the two paradigms we survey all the results that have been recorded in the literature with regard to each type of machine eligibility constraints. We obtain also several extensions in various directions. In the concluding section we describe the most important open problems in this particular area.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
£29.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (United Kingdom)

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  • Albers, S. (2003). Online algorithms: a survey. Mathematical Programming Series B, 97, 3–26.

    Google Scholar 

  • Azar, Y., Naor, J., & Rom, R. (1995). The competitiveness of on-line assignments. Journal of Algorithms, 18, 221–237.

    Article  Google Scholar 

  • Bar-Noy, A., Freund, A., & Naor, J. (2001). Online load balancing in a hierarchical server topology. SIAM Journal on Computing, 31, 527–549.

    Article  Google Scholar 

  • Chassid, O., & Epstein, L. (2008). The hierarchical model for load balancing on two machines. Journal of Combinatorial Optimization, 15, 305–314.

    Article  Google Scholar 

  • Chen, B., & Vestjens, A. P. A. (1997). Scheduling on identical machines: how good is LPT in an on-line setting? Operations Research Letters, 21, 165–169.

    Article  Google Scholar 

  • Dosa, G., & Epstein, L. (2008). Preemptive scheduling on a small number of hierarchical machines. Information and Computation, 206(5), 602–619.

    Article  Google Scholar 

  • Garg, N., & Kumar, A. (2007). Minimizing average flow-time: upper and lower bounds. In Proceedings of the 48th annual IEEE symposium on foundations of computer science (pp. 603–613).

    Google Scholar 

  • Glass, C. A., & Mills, H. R. (2006). Scheduling unit length jobs with parallel nested machine processing set restrictions. Computers & Operations Research, 33, 620–638.

    Article  Google Scholar 

  • Graham, R. L., Lawler, E. L., Lenstra, J. K., & Rinnooy Kan, A. H. G. (1979). Optimization and approximation in deterministic sequencing and scheduling: a survey. Annals of Discrete Mathematics, 5, 287–326.

    Article  Google Scholar 

  • Hall, L. A., Schulz, A. S., Shmoys, D. B., & Wein, J. (1997). Scheduling to minimize average completion time: off-line and on-line approximation algorithms. Mathematics of Operations Research, 22(3), 513–544.

    Article  Google Scholar 

  • Hong, K. S., & Leung, J. Y.-T. (1992). On-line scheduling of real-time tasks. IEEE Transactions on Computers, 41, 1326–1331.

    Article  Google Scholar 

  • Hou, L., & Kang, L. (2011). Online and semi-online hierarchical scheduling for load balancing on uniform machines. Theoretical Computer Science, 412, 1092–1098.

    Article  Google Scholar 

  • Hou, L., & Kang, L. (2012). Online scheduling on uniform machines with two hierarchies. Journal of Combinatorial Optimization, 24(4), 593–612.

    Article  Google Scholar 

  • Hwang, H.-C., Chang, S. Y., & Hong, Y. (2004a). A posterior competitiveness for list scheduling algorithm on machines with eligibility constraints. Asia-Pacific Journal of Operational Research, 21, 117–125.

    Article  Google Scholar 

  • Hwang, H.-C., Chang, S. Y., & Lee, K. (2004b). Parallel machine scheduling under a grade of service provision. Computers & Operations Research, 31, 2055–2061.

    Article  Google Scholar 

  • Huo, Y., & Leung, J. Y.-T. (2010a). Parallel machine scheduling with nested processing set restrictions. European Journal of Operational Research, 204, 229–236.

    Article  Google Scholar 

  • Huo, Y., & Leung, J. Y.-T. (2010b). Fast approximation algorithms for job scheduling with processing set restrictions. Theoretical Computer Science, 411(44–46), 3947–3955.

    Article  Google Scholar 

  • Jiang, Y. (2008). Online scheduling on parallel machines with two GoS levels. Journal of Combinatorial Optimization, 16, 28–38.

    Article  Google Scholar 

  • Jiang, Y., He, Y., & Tang, C. (2006). Optimal online algorithms for scheduling on two identical machines under a grade of service. Journal of Zhejiang University. Science A, 7, 309–314.

    Article  Google Scholar 

  • Karhi, S., & Shabtay, D. (2012). On the optimality of the TLS algorithm for solving the online-list scheduling problem with two job types on a set of multipurpose machines. Journal of Combinatorial Optimization. doi:10.1007/s10878-012-9460-4.

    Google Scholar 

  • Lawler, E. L., & Labetoulle, J. (1978). On preemptive scheduling of unrelated parallel processors by linear programming. Journal of the ACM, 25(4), 612–619.

    Article  Google Scholar 

  • Lee, K., Leung, J. Y.-T., & Pinedo, M. (2009). Online scheduling on two uniform machines subject to eligibility constraints. Theoretical Computer Science, 410, 3975–3981.

    Article  Google Scholar 

  • Lee, K., Leung, J. Y.-T., & Pinedo, M. (2010). Makespan minimization in online scheduling with machine eligibility. 4OR, 8(4), 331–364.

    Article  Google Scholar 

  • Lee, K., Leung, J. Y.-T., & Pinedo, M. (2011). Scheduling jobs with equal processing times subject to machine eligibility constraints. Journal of Scheduling, 14(1), 27–38.

    Article  Google Scholar 

  • Lenstra, J. K., Shmoys, D. B., & Tardos, E. (1990). Approximation algorithms for scheduling unrelated parallel machines. Mathematical Programming, 46, 259–271.

    Article  Google Scholar 

  • Leung, J. Y.-T., & Li, C.-L. (2008). Scheduling with processing set restrictions: a survey. International Journal of Production Economics, 116, 251–262.

    Article  Google Scholar 

  • Lim, K., Lee, K., & Chang, S. Y. (2011). Improved bounds for online scheduling with eligibility constraints. Theoretical Computer Science, 412(39), 5211–5224. (Working paper title: On optimality of a greedy approach to the online scheduling under eligibility constraints).

    Article  Google Scholar 

  • Liu, M., Xu, Y., Chu, C., & Zheng, F. (2009). Online scheduling on two uniform machines to minimize the makespan. Theoretical Computer Science, 410(21–23), 2099–2109.

    Article  Google Scholar 

  • Liu, M., Chu, C., Xu, Y., & Zheng, F. (2011). Semi-online scheduling on 2 machines under a grade of service provision with bounded processing times. Journal of Combinatorial Optimization, 21(1), 138–149.

    Article  Google Scholar 

  • Mandelbaum, M., & Shabtay, D. (2011). Scheduling unit length jobs on parallel machines with lookahead information. Journal of Scheduling, 14(4), 335–350.

    Article  Google Scholar 

  • McNaughton, R. (1959). Scheduling with deadlines and loss functions. Management Science, 6, 1–12.

    Article  Google Scholar 

  • Muratore, G., Schwarz, U. M., & Woeginger, G. J. (2010). Parallel machine scheduling with nested job assignment restrictions. Operations Research Letters, 38(1), 47–50.

    Article  Google Scholar 

  • Noga, J., & Seiden, S. S. (2001). An optimal online algorithm for scheduling two machines with release times. Theoretical Computer Science, 268, 133–143.

    Article  Google Scholar 

  • Ou, J., Leung, J. Y.-T., & Li, C.-L. (2008). Scheduling parallel machines with inclusive processing set restriction. Naval Research Logistics, 55(4), 328–338.

    Article  Google Scholar 

  • Park, J., Chang, S. Y., & Lee, K. (2006). Online and semi-online scheduling of two machines under a grade of service provision. Operations Research Letters, 34, 692–696.

    Article  Google Scholar 

  • Pruhs, K., Sgall, J., & Torng, E. (2004). Online scheduling. In J. Y.-T. Leung (Ed.), Handbook of scheduling: algorithms, models, and performance analysis. Boca Raton: CRC Press.

    Google Scholar 

  • Sgall, J. (1998). On-line scheduling. In Lecture notes in computer science (Vol. 1442, pp. 196–231).

    Google Scholar 

  • Shabtay, D., & Karhi, S. (2012a). Online scheduling of two job types on a set of multipurpose machines with unit processing times. Computers & Operations Research, 39, 405–412.

    Article  Google Scholar 

  • Shabtay, D., & Karhi, S. (2012b, submitted). Online scheduling of two job types on a set of multipurpose machines (Working Paper).

  • Shchepin, E. V., & Vakhania, N. (2005). An optimal rounding gives a better approximation for scheduling unrelated machines. Operations Research Letters, 33, 127–133.

    Article  Google Scholar 

  • Shmoys, D. B., Wein, J., & Williamson, D. P. (1995). Scheduling parallel machines on-line. SIAM Journal on Computing, 24(6), 1313–1331.

    Article  Google Scholar 

  • Tan, Z., & Zhang, A. (2010). A note on hierarchical scheduling on two uniform machines. Journal of Combinatorial Optimization, 20(1), 85–95.

    Article  Google Scholar 

  • Tan, Z., & Zhang, A. (2011). Online hierarchical scheduling: an approach using mathematical programming. Theoretical Computer Science, 412(3), 246–256.

    Article  Google Scholar 

  • Wang, Z., & Xing, W. (2010). Worst-case analysis for on-line service polices. Journal of Combinatorial Optimization, 19, 107–122.

    Article  Google Scholar 

  • Wang, Z., Xing, W., & Chen, B. (2009). On-line service scheduling. Journal of Scheduling, 12(1), 31–43.

    Article  Google Scholar 

  • Wu, Y., Ji, M., & Yang, Q. (2012). Optimal semi-online scheduling algorithms on two parallel identical machines under a grade of service provision. International Journal of Production Economics, 135(1), 367–371.

    Article  Google Scholar 

  • Zhang, A., Jiang, Y., & Tan, Z. (2008). Optimal algorithms for online hierarchical scheduling on parallel machines (Technical Report). Zhejiang University.

  • Zhang, A., Jiang, Y., & Tan, Z. (2009). Online parallel machines scheduling with two hierarchies. Theoretical Computer Science, 410, 3597–3605.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Supply Chain Management & Marketing Sciences, Rutgers Business School, 1 Washington Park, Newark, NJ, 07102-3122, USA

    Kangbok Lee

  2. Department of Computer Science, New Jersey Institute of Technology, Newark, NJ, 07102, USA

    Joseph Y.-T. Leung

  3. Department of Information, Operations & Management Sciences, Stern School of Business, New York University, 44 West 4th Street, New York, NY, 10012-1126, USA

    Michael L. Pinedo

Authors
  1. Kangbok Lee
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Joseph Y.-T. Leung
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Michael L. Pinedo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Michael L. Pinedo.

Additional information

This is an updated version of the paper that appeared in 4OR, 8(4), 331–364 (2010).

Work of J.Y.-T.L. is supported in part by the NSF Grant CMMI-0969830.

Work of M.L.P. is supported in part by the NSF Grant CMMI-0969755.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lee, K., Leung, J.YT. & Pinedo, M.L. Makespan minimization in online scheduling with machine eligibility. Ann Oper Res 204, 189–222 (2013). https://doi.org/10.1007/s10479-012-1271-6

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10479-012-1271-6

Keywords

Search

Navigation