An O(n 2 ) algorithm for scheduling equal-length preemptive jobs on a single machine to minimize total tardiness
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In this paper, we study the problem of scheduling n equal-length preemptive jobs on a single machine to minimize total tardiness, subject to release dates. The complexity status of this problem has remained open to date. We provide an O(n 2) time algorithm to solve the problem.
KeywordsSingle machine Preemptive scheduling Release date Equal-length jobs Total tardiness
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- Baker, K. R., E. L. Lawler, J. K. Lenstra and A. H. G. Rinnooy Kan, “Preemptive Scheduling of a Single Machine to Minimize Maximum Cost Subject to Release Dates and Precedence Constraints,” Operations Research, 31, 381–386 (1983).Google Scholar
- Brucker, P. and S. Knust, “Complexity Results for Scheduling Problems,” URL: http://waw.mathematik.uni-osnabrueck.de/research/OR/class.
- Chen, B., C. Potts and G. Woeginger, “A Review of Machine Scheduling: Complexity, algorithms and approximability,” Handbook of Combinatorial Optimization, Kluwer Academic Publishers, Boston, 1998, pp. 21–169.Google Scholar
- Chu, C., “A Branch-And-Bound Algorithm to Minimize Total Tardiness with Different Release Dates,” Naval Research Logistics, 39, 265–283 (1992).Google Scholar
- Gordon, V. S. and V. S. Tanaev, “On minimax problems of scheduling theory for a single machine (in Russian),” Vetsi Akadeii Navuk BSSR. Ser. fizika-matematychnykh navuk, 1983, pp. 3–9.Google Scholar
- Graham, R. L., E. L. Lawler, J. K. Lenstra and A. H. G. Rinnooy Kan, “Optimization and approximation in Deterministic Sequencing and Scheduling: A Survey,” Annals of Operations Research, 5, 287–326 (1979).Google Scholar
- Labetoulle, J., E. L. Lawler, J. K. Lenstra and A. H. G. Rinnooy Kan, “Preemptive Scheduling of Uniform Machines Subject to Release Dates,” Progress in Combinatorial Optimization, Academic Press, New York, 1984, pp. 245–261.Google Scholar
- Pinedo, M., Scheduling: Theory, Algorithms, and Aystems. Prentice Hall, New Jersey, 1995.Google Scholar