Advertisement

Journal of Scheduling

, Volume 19, Issue 2, pp 207–211 | Cite as

A note on longest processing time algorithms for the two uniform parallel machine makespan minimization problem

  • Ivar Massabò
  • Giuseppe Paletta
  • Alex J. Ruiz-Torres
Article

Abstract

This note considers the longest processing time heuristic for scheduling n independent jobs on two uniform parallel machines to minimize the makespan. A posterior worst-case performance ratio, by depending on the index of the latest job inserted in the machine where the makespan takes place, is developed for this heuristic, and some examples demonstrate that the ratio is tight.

Keywords

Scheduling Two uniform parallel machines LPT schedule Heuristic 

References

  1. Blocher, J. D., & Chand, S. (1991). Scheduling of parallel processors: A posterior bound on LPT sequencing and a two-step algorithm. Naval Research Logistics, 38(2), 273–287.CrossRefGoogle Scholar
  2. Blocher, J. D., & Sevastyanov, S. (2015). A note on the Coffman–Sethi bound for LPT scheduling. Journal of Scheduling, 18(3), 325–327.CrossRefGoogle Scholar
  3. Burkard, R. E., & He, Y. (1998). A note on MULTIFIT scheduling for uniform machines. Computing, 61, 277–283.CrossRefGoogle Scholar
  4. Chen, B. (1991a). Parametric bounds for LPT scheduling on uniform processors. Acta Mathematicae Applicatae Sinica, 7, 67–73.Google Scholar
  5. Chen, B. (1991b). Tighter bound for MULTIFIT scheduling on uniform processors. Discrete Applied Mathematics, 31, 227–260.Google Scholar
  6. Chen, B. (1993). A note on LPT scheduling. Operations Research Letters, 14, 139–142.CrossRefGoogle Scholar
  7. Coffman, E. G, Jr., Garey, M. R., & Johnson, D. S. (1978). An application of bin-paking to multiprocessor scheduling. SIAM Journal on Computing, 7, 1–17.Google Scholar
  8. Coffman, E. G, Jr., & Sethi, R. (1976a). A generalized bound on LPT sequencing. Revue Française d’ Automatique Informatique, Recherche Operationnelle Supplément, 10, 17–25.Google Scholar
  9. Coffman, E. G. Jr., Sethi, R. (1976b). A generalized bound on LPT sequencing. Proceedings of the International Symposium on Computer Performance Modeling (pp. 306–310).Google Scholar
  10. Dobson, G. (1984). Scheduling independent tasks on uniform processors. SIAM Journal on Computing, 13, 705–716.CrossRefGoogle Scholar
  11. Friesen, D. K. (1987). Tighter bounds for LPT scheduling on uniform processors. SIAM Journal on Computing, 16, 554–560.CrossRefGoogle Scholar
  12. Friesen, D. K., & Langston, M. A. (1983). Bounds for MULTIFIT scheduling on uniform processors. SIAM Journal on Computing, 12, 60–70.CrossRefGoogle Scholar
  13. Garey, M. R., & Johnson, D. S. (1979). Computers and intractability: A guide to the theory of NP-completeness. San Francisco: The W.H. Freeman and Company.Google Scholar
  14. Gonzalez, T., Ibarra, O. H., & Sahni, S. (1977). Bounds for LPT schedules on uniform processors. SIAM Journal on Computing, 6, 155–166.CrossRefGoogle Scholar
  15. Graham, R. L. (1966). Bounds for certain multiprocessing anomalies. Bell System Technical Journal, 45, 1563–1581.CrossRefGoogle Scholar
  16. Graham, R. L. (1969). Bounds on multiprocessing timing anomalies. SIAM Journal on Applied Mathematics, 17, 416–429.CrossRefGoogle Scholar
  17. 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.CrossRefGoogle Scholar
  18. Koulamas, C., & Kyparisis, G. J. (2009). A modified LPT algorithm for the two uniform parallel machine makespan minimization problem. European Journal of Operational Research, 196, 61–68.CrossRefGoogle Scholar
  19. Mireault, P., Orlin, J. B., & Vohra, R. V. (1997). A parametric worst case analysis of the LPT heuristic for two uniform machines. Operations Research, 45, 116–125.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Ivar Massabò
    • 1
  • Giuseppe Paletta
    • 1
  • Alex J. Ruiz-Torres
    • 2
  1. 1.Dipartimento di Economia Statistica e FinanzaUniversità della CalabriaArcavacata di RendeItaly
  2. 2.Departamento de Gerencia, Facultad de Administración de EmpresasUniversidad de Puerto Rico - Rio PiedrasSan JuanUSA

Personalised recommendations