4OR

, Volume 8, Issue 4, pp 331–364 | Cite as

Makespan minimization in online scheduling with machine eligibility

  • Kangbok Lee
  • Joseph Y.-T. Leung
  • Michael L. Pinedo
Invited Survey

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.

Keywords

Parallel machine scheduling Eligibility constraint Tree-hierarchical and GoS processing sets Interval and nested processing sets Online and Semi-online scheduling Offline scheduling Makespan Competitive ratio 

MSC classification (2000)

90B35: Scheduling theory, deterministic 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Albers S (2003) Online algorithms: a survey. Math Program Ser B 97: 3–26Google Scholar
  2. Azar Y, Naor J, Rom R (1995) The competitiveness of on-line assignments. J Algorithm 18: 221–237CrossRefGoogle Scholar
  3. Bar-Noy A, Freund A, Naor J (2001) Online load balancing in a hierarchical server topology. SIAM J Comput 31: 527–549CrossRefGoogle Scholar
  4. Chen B, Vestjens APA (1997) Scheduling on identical machines: how good is LPT in an on-line setting?. Oper Res Lett 21: 165–169CrossRefGoogle Scholar
  5. Dosa G, Epstein L (2008) Preemptive scheduling on a small number of hierarchical machines. Inf Comput 206(5): 602–619CrossRefGoogle Scholar
  6. 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 603–613Google Scholar
  7. Glass CA, Mills HR (2006) Scheduling unit length jobs with parallel nested machine processing set restrictions. Comput Oper Res 33: 620–638CrossRefGoogle Scholar
  8. Graham RL, Lawler EL, Lenstra JK, Rinnooy Kan AHG (1979) Optimization and approximation in deterministic sequencing and scheduling: a survey. Ann Discret Math 5: 287–326CrossRefGoogle Scholar
  9. Hall LA, Schulz AS, Shmoys DB, Wein J (1997) Scheduling to minimize average completion time: off-line and on-line approximation algorithms. Math Oper Res 22(3): 513–544CrossRefGoogle Scholar
  10. Hong KS, Leung JY-T (1992) On-line scheduling of real-time tasks. IEEE Trans Comput 41: 1326–1331CrossRefGoogle Scholar
  11. Huo Y, Leung JY-T (2010a) Parallel machine scheduling with nested processing set restrictions. Eur J Oper Res 204: 229–236CrossRefGoogle Scholar
  12. Huo Y, Leung JY-T (2010b) Fast approximation algorithms for job scheduling with processing set restrictions, Theoretical Computer Science, to appear. doi:10.1016/j.tcs.2010.08.008
  13. Hwang H-C, Chang SY, Hong Y (2004) A posterior competitiveness for list scheduling algorithm on machines with eligibility constraints. Asia-Pac J Oper Res 21: 117–125CrossRefGoogle Scholar
  14. Hwang H-C, Chang SY, Lee K (2004) Parallel machine scheduling under a grade of service provision. Comput Oper Res 31: 2055–2061CrossRefGoogle Scholar
  15. Jiang Y (2008) Online scheduling on parallel machines with two GoS levels. J Comb Optim 16: 28–38CrossRefGoogle Scholar
  16. Jiang Y, He Y, Tang C (2006) Optimal online algorithms for scheduling on two identical machines under a grade of service. J Zhejiang Univ Sci A 7: 309–314CrossRefGoogle Scholar
  17. Lawler EL, Labetoulle J (1978) On preemptive scheduling of unrelated parallel processors by linear programming. J ACM 25(4): 612–619CrossRefGoogle Scholar
  18. Lee K, Leung JY-T, Pinedo M (2009) Online scheduling on two uniform machines subject to eligibility constraints. Theor Comput Sci 410: 3975–3981CrossRefGoogle Scholar
  19. Lee K, Leung JY-T, Pinedo M (2010) Scheduling jobs with equal processing times subject to machine eligibility constraints. J Sched, to appear. doi:10.1007/s10951-010-0190-0
  20. Lenstra JK, Shmoys DB, Tardos E (1990) Approximation algorithms for scheduling unrelated parallel machines. Math Program 46: 259–271CrossRefGoogle Scholar
  21. Leung JY-T, Li C-L (2008) Scheduling with processing set restrictions: a survey. Int J Prod Econ 116: 251–262Google Scholar
  22. Lim K, Lee K, Chang SY (2010) On optimality of a greedy approach to the online scheduling under eligibility constraints, Working paper, Department of Industrial and Management Engineering, Pohang University of Science and Technology, Republic of Korea 790–784Google Scholar
  23. Liu M, Xu Y, Chu C, Zheng F (2009) Online scheduling on two uniform machines to minimize the makespan. Theor Comput Sci 410(21–23): 2099–2109CrossRefGoogle Scholar
  24. Liu M, Chu C, Xu Y, Zheng F (2010) Semi-online scheduling on 2 machines under a grade of service provision with bounded processing times. J Comb Optim, to appear. doi:10.1007/s10878-009-9231-z
  25. Mandelbaum M, Shabtay D (2010) Scheduling unit length jobs on parallel machines with lookahead information. J Sched, to appear. doi:10.1007/s10951-010-0192-y
  26. McNaughton R (1959) Scheduling with deadlines and loss functions. Manag Sci 6: 1–12CrossRefGoogle Scholar
  27. Muratore G, Schwarz UM, Woeginger GJ (2010) Parallel machine scheduling with nested job assignment restrictions. Oper Res Lett 38(1): 47–50CrossRefGoogle Scholar
  28. Noga J, Seiden SS (2001) An optimal online algorithm for scheduling two machines with release times. Theor Comput Sci 268: 133–143CrossRefGoogle Scholar
  29. Ou J, Leung JY-T, Li C-L (2008) Scheduling parallel machines with inclusive processing set restriction. Nav Res Logist 55(4): 328–338CrossRefGoogle Scholar
  30. 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: 692–696CrossRefGoogle Scholar
  31. Pruhs K, Sgall J, Torng E (2004) Online scheduling. In: Leung JY-T (ed) Handbook of scheduling: algorithms, models, and performance analysis. CRC Press, Boca RatonGoogle Scholar
  32. Sgall J (1998) On-line scheduling. Lecture Notes in Computer Science 1442: 196–231CrossRefGoogle Scholar
  33. Shchepin EV, Vakhania N (2005) An optimal rounding gives a better approximation for scheduling unrelated machines. Oper Res Lett 33: 127–133CrossRefGoogle Scholar
  34. Shmoys DB, Wein J, Williamson DP (1995) Scheduling parallel machines on-line. SIAM J Comput 24(6): 1313–1331CrossRefGoogle Scholar
  35. Tan Z, Zhang A (2010a) A note on hierarchical scheduling on two uniform machines. J Comb Optim 20(1): 85–95CrossRefGoogle Scholar
  36. Tan Z, Zhang A (2010b) Online hierarchical scheduling: an approach using mathematical programming. Theorl Comput Sci. doi:10.1016/j.tcs.2009.08.014 Google Scholar
  37. Wang Z, Xing W (2010) Worst-case analysis for on-line service polices. J Comb Optim 19: 107–122CrossRefGoogle Scholar
  38. Wang Z, Xing W, Chen B (2009) On-line service scheduling. J Sched 12(1): 31–43CrossRefGoogle Scholar
  39. Wu Y, Yang Q (2010) Optimal semi-online scheduling algorithms on two parallel identical mamchhines under a Grade of Service provision. Lecture Notes in Computer Science 6124: 261–270CrossRefGoogle Scholar
  40. Zhang A, Jiang Y, Tan Z (2009) Online parallel machines scheduling with two hierarchies. Theor Comput Sci 410: 3597–3605CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  • Kangbok Lee
    • 1
  • Joseph Y.-T. Leung
    • 2
  • Michael L. Pinedo
    • 3
  1. 1.Department of Supply Chain Management and Marketing SciencesRutgers Business SchoolNewarkUSA
  2. 2.Department of Computer ScienceNew Jersey Institute of TechnologyNewarkUSA
  3. 3.Department of Information, Operations and Management Sciences, Stern School of BusinessNew York UniversityNew YorkUSA

Personalised recommendations