Bi-criteria Scheduling on Multiple Machines Subject to Machine Availability Constraints

  • Yumei Huo
  • Hairong Zhao
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7924)

Abstract

This paper studies bi-criteria scheduling problems on m parallel machines with machine unavailable intervals. The goal is to minimize the total completion time subject to the constraint that the makespan is at most a constant T. We study two different unavailability models. In the first model, each machine has a single unavailable interval which starts from time 0. In the second model, each machine can have multiple unavailable intervals, but at any time, there is at most one machine unavailable. For each model, we show that there is an optimal polynomial time algorithm.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Chen, C.L., Bulfin, R.L.: Complexity of single machine, multicriteria scheduling problems. European Journal of Operational Research 70, 115–125 (1993)MATHCrossRefGoogle Scholar
  2. 2.
    Dileepan, P., Sen, T.: Bicriteria static scheduling research for a single machine. OMEGA 16, 53–59 (1988)CrossRefGoogle Scholar
  3. 3.
    Graham, R.L., Lawler, E.L., Lenstra, J.K., Rinnooy Kan, A.H.G.: Optimization and approximation in deterministic sequencing and scheduling, a survey. Annals of Discrete Mathematics 5, 287–326 (1979)MathSciNetMATHCrossRefGoogle Scholar
  4. 4.
    Gupta, J.N.D., Ho, J.C., Webster, S.: Bicriteria optimisation of the makespan and mean flowtime on two identical parallel machines. Journal of Operational Research Society 51(11), 1330–1339 (2000)MATHGoogle Scholar
  5. 5.
    Hoogeveen, J.A.: Multicriteria scheduling. European Journal of Operational Research 167(3), 592–623 (2005)MathSciNetMATHCrossRefGoogle Scholar
  6. 6.
    Huo, Y., Zhao, H.: Bicriteria Scheduling Concerned with Makespan and Total Completion Time Subject to Machine Availability Constraints. Theoretical Computer Science 412, 1081–1091 (2011)MathSciNetMATHCrossRefGoogle Scholar
  7. 7.
    Leung, J.Y.-T., Young, G.H.: Minimizing schedule length subject to minimum flow time. SIAM Journal on Computing 18(2), 314–326 (1989)MathSciNetMATHCrossRefGoogle Scholar
  8. 8.
    Leung, J.Y.-T., Pinedo, M.L.: Minimizing total completion time on parallel machines with deadline constraints. SIAM Journal on Computing 32, 1370–1388 (2003)MathSciNetMATHCrossRefGoogle Scholar
  9. 9.
    Leung, J.Y.-T., Pinedo, M.L.: A Note on the scheduling of parallel machines subject to breakdown and repair. Naval Research Logistics 51, 60–72 (2004)MathSciNetMATHCrossRefGoogle Scholar
  10. 10.
    Ma, Y., Chu, C., Zuo, C.: A survey of scheduling with deterministic machine availability constraints. Computers & Industrial Engineering 58(2), 199–211 (2010)CrossRefGoogle Scholar
  11. 11.
    Liu, Z., Sanlaville, E.: Preemptive scheduling with variable profile, precedence constraints and due dates. Discrete Applied Mathematics 58, 253–280 (1995)MathSciNetMATHCrossRefGoogle Scholar
  12. 12.
    Saidy, H., Taghvi-Fard, M.: Study of Scheduling Problems with Machine Availability Constraint. Journal of Industrial and Systems Engineering 1(4), 360–383 (2008)Google Scholar
  13. 13.
    Schmidt, G.: Scheduling with limited machine availability. European Journal of Operational Research 121(1), 1–15 (2000)MathSciNetMATHCrossRefGoogle Scholar
  14. 14.
    T’kindt, V., Billaut, J.C.: Multicriteria Scheduling: Theory, Models and Algorithms. Springer, Heidelberg (2002)MATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Yumei Huo
    • 1
  • Hairong Zhao
    • 2
  1. 1.Department of Computer Science, College of Staten IslandCUNYStaten IslandUSA
  2. 2.Department of Mathematics, Computer Science & StatisticsPurdue University CalumetHammondUSA

Personalised recommendations