Abstract
In this note we investigate the NP-complete problem of minimizing the makespan in a preemptive two machine job shop. We present a polynomial time approximation algorithm with worst case ratio 3/2 for this problem, and we also argue that this is the best possible result that can be derived via our line of approach.
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.References
Akers, S. B.: A graphical approach to production scheduling problems. Oper. Res.4, 244–245 (1956).
Brucker, P., Kravchenko, S. A., Sotskov, Y. N.: Preemptive job-shop scheduling problems with a fixed number of jobs. Osnabrücker Schriften zur Mathematik,184, Universität Osnabrück, Germany (1997).
Gonzalez, T., Sahni, S.: Flowshop and jobshop schedules: complexity and approximation. Oper. Res.26, 36–52 (1978).
Graham, R. L.: Bounds on multiprocessing timing anomalies. SIAM J. Appl. Math.17, 416–429 (1969).
Hall, L. A.: Approximability of flow shop scheduling. In: Proceedings of 36th IEEE Symposium on Foundations of Computer Science, pp. 82–91 (1995).
Hefetz, N., Adiri, I.: An efficient optimal algorithm for the two-machine, unit-time, jobshop, schedule-length problem. Math. Oper. Res.7, 354–360 (1982).
Jackson, J. R.: An extension of Johnson’s result on job lot scheduling. Naval. Res. Log. Q.3, 201–203 (1956).
Lawler, E. L., Lenstra, J. K., Rinnooy Kan, A. H. G., Shmoys, D. B.: Sequencing and scheduling: algorithms and complexity. In: Handbooks in Operations Research and Management Science, Vol. 4, pp. 445–522. Amsterdam: North Holland, 1993.
Sevastianov, S. V., Woeginger, G. J.: Makespan minimization in open shops: a polynomial time approximation scheme. Math. Program. to appear (1997).
Shmoys, D. B., Stein, C., Wein, J.: Improved approximation algorithm for shop scheduling problems. SIAM. J. Comput.23, 617–632 (1996).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Sevastianov, S.V., Woeginger, G.J. Makespan minimization in preemptive two machine job shops. Computing 60, 73–79 (1998). https://doi.org/10.1007/BF02684330
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02684330