Abstract
In this paper we present constructive algorithms for the classical deterministic scheduling problem of minimizing the makespan on identical machines. Since the problem is known to beNP-hard in the strong sense, the approximate algorithms play a relevant role when solving this problem. The proposed algorithms are based on list scheduling procedures, but the assignment rule is not the same for the full set of jobs. Computational results show that these algorithms perform very well.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Achugbue J.O. and Chin F.Y. (1981). Bounds on schedules for independent tasks with similar execution time.Journal of the Association for Computing Machinery 28, 81–99.
Arora S. and Lund C. (1997). Hardness of Approximations. In: Hochbaum D.S. (ed.),Approximation Algorithms for NP-hard Problems. PWS, 399–446.
Coffman E.G. Jr., Garey M.R. and Johnson D.S. (1978). An application of Bin-Packing to multiprocessor scheduling.SIAM Journal on Computing 7, 1–17.
Cook S.A. (1971). The complexity of theorem-proving procedures.Proceedings of the 3rd Annual ACM Symposium on Theory of Computing, 151–158.
De P. and Morton T.E. (1980). Scheduling to minimum makespan on unequal parallel processors.Decision Science 11, 586–602.
Dobson G. (1984). Scheduling independent tasks on uniform processors.SIAM Journal of Computing 13, 705–716.
França P.M., Gendreau M., Laporte G. and Müller F.M. (1994). A composite heuristic for the identical parallel machine scheduling problem with minimum makespan objective.Computers and Operations Research 21, 205–210.
Frenk J. and Rinnooy Kan A.H.G. (1984a). The asymptotic optimality of the LPT scheduling heuristic. Report, Erasmus University, Rotterdam.
Frenk J. and Rinnooy Kan A.H.G. (1984b). The rate of convergence to optimality of the LPT scheduling heuristic. Report, Erasmus University, Rotterdam.
Graham R.L. (1966). Bounds for certain multiprocessing anomalies.Bell System Technical Journal 45, 1563–1581.
Graham R.L. (1969). Bounds on multiprocessing timing anomalies.SIAM Journal on Applied Mathematics 17, 263–269.
Graham R.L., Lawler E.L., Lenstra J.K. and Rinnooy Kan A.H.G. (1979). Optimization and approximation in deterministic sequencing and scheduling. A survey.Annals of Discrete Mathematics 5, 287–326.
Han S., Hong D. and Leung J.Y.T. (1995). On the asymptotic optimality of multiprocessor scheduling heuristics for the makespan minimization problem.ORSA Journal on Computing 2, 201–204.
Haupt R. (1989). A survey of priority rule-based scheduling.Operational Research Spektrum 11, 3–16.
Hübscher R. and Glover F. (1994). Applying Tabu Search with influential diversification to multiprocessor scheduling.Computers Operations Research 8, 877–884.
Ibarra O.H. and Kim C.E. (1976). On two processor scheduling of one-or two-unit time tasks with precedence constraints.Journal of Cybernetics 5, 87–109.
Karp R.M. (1972). Reducibility among combinatorial problems. In: Miller R.E. and Tatcher J.W. (eds.),Complexity of Computer Computations. Plenum Press, 85–103.
Lenstra J.K. and Rinnooy Kan A.H.G. (1979). Computational complexity of discrete optimization. In: Lenstra J.K., Rinnooy Kan A.H.G. and Van Emde Boas P. (eds.),Interfaces Between Computer Science and Operations Research. Proceedings of a Symposium held at the Matematisch Centrum, Amsterdam, 64–85.
Lenstra J.K. and Shmoys D.B. (1995). Computing near-optimal schedules. In: Chrétienne P., Coffman E.G. Jr., Lenstra J.K. and Liu Z. (eds.),Scheduling Theory and its Applications. Wiley, 1–14.
McNaughton R. (1959). Scheduling with deadlines and loss function.Management Science 6, 1–12.
Mokotoff E. (1998). Metodologías de Resolución de Problemas de Asignación y Ordenación de Tareas a Recursos: Planificación con Recursos Idénticos (in Spanish). PhD Thesis, Universidad de Alcalá.
Mokotoff E. (1999). Scheduling to Minimize the Makespan on Identical Parallel Machines: An LP-Based Algorithm.Investigación Operativa 8, 97–108.
Mokotoff E. (2001). Parallel Machine Scheduling Problems: A Survey.Asia-Pacific Journal of Operational Research 18, 193–243.
Panwalkar S.S. and Iskander W. (1977). A survey of scheduling rules.Operations Research 25, 45–61.
Riera J., Alcaide D. and Sicilia J. (1996). Approximate algorithms for theP//C max problem.Top 4, 345–359.
Sahni S. (1977). General techniques for combinatorial optimization.Operations Research 25, 920–936.
Sotskov Y.N. and Shaklevich N.V. (1995). NP-hardness of shop scheduling problems with three jobs.Discrete Applied Mathematics 59, 237–266.
Weiss G. (1995). On almost optimal priority rules for preemptive scheduling of stochastic jobs on parallel machines.Advances in Applied Probability 27, 821–839.
Author information
Authors and Affiliations
Additional information
This research has been partially supported by the Research Project H015/2000, Universidad de Alcalá. The authors are indebted to Joaquín Pérez and the referees for their helpful remarks and comments. We also wish to thank Paul Alexander Ayres for his help in the correct use of English.
Rights and permissions
About this article
Cite this article
Mokotoff, E., Jimeno, J.L. & Gutiérrez, A.I. List scheduling algorithms to minimize the makespan on identical parallel machines. Top 9, 243–269 (2001). https://doi.org/10.1007/BF02579085
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF02579085