Abstract
We prove that the problem P ∣ p i = p, pmtn ∣ ∑w i U i is unary NP-hard although the corresponding nonpreemptive problem can be solved in O(n log n) time, where n is the number of jobs. This contrasts the fact that usually preemptive problems are not harder than their nonpreemptive counterparts.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Brucker, P.: Scheduling algorithms. Springer, Berlin Heidelberg New York Tokyo, 1998.
Brucker, P., Jurisch, B. and Jurisch, M.: Open shop problems with unit time operations, Math. Methods Oper. Res. 37 (1993), 59–73.
Brucker, P., Kravchenko, S. A. and Sotskov, Y. N.: Preemptive job-shop scheduling problem with a fixed number of jobs, Math. Methods Oper. Res. 49 (1999), 41–76.
Garey, M. R. and Johnson, D. S.: Computers and intractability. A guide to the theory of NP-completeness. W.H. Freeman and Company, San Francisco, 1979.
Lawler, E. L.: Resent results in the theory of machine scheduling, in A. Bachem, M. Grötschel and B. Korte (eds.), Mathematical Programming: the State of the Art, Springer, Berlin Heidelberg New York Tokyo, 1983, pp. 202–234.
Author information
Authors and Affiliations
Corresponding author
Additional information
*Supported by the Alexander von Humboldt Foundation.
Rights and permissions
About this article
Cite this article
Brucker, P., Kravchenko, S.A. Scheduling Equal Processing Time Jobs to Minimize the Weighted Number of Late Jobs. J Math Model Algor 5, 143–165 (2006). https://doi.org/10.1007/s10852-005-9011-4
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10852-005-9011-4