Abstract
In this paper we give a polynomial algorithm for the problem P | r i , p i =p, pmtn | ∑ C i . This result is applied to derive a polynomial algorithm for the problem O | r i , p ij =1| ∑ C i .
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Baptiste, P., Brucker, P.: Scheduling Equal Processing Time Jobs: A Survey. In: Leung, Y.T. (ed.) Handbook of Scheduling: Algorithms, Models, and Performance Analysis, pp. 78–96. CRC Press LLC, Boca Raton (2004)
Brucker, P., Jurisch, B., Jurisch, M.: Open shop problems with unit time operations. Z. Oper. Res. 37, 59–73 (1993)
Brucker, P.: Scheduling Algorithms, 3rd edn. Springer, Berlin (2001)
Chvatal, V.: Linear programming. Freeman, New York (1983)
Du, J., Leung, J.Y.-T., Young, G.H.: Minimizing mean flow time with release time constraint. Theoretical Computer Science 75, 347–355 (1990)
Garey, M.R., Johnson, D.S.: Computers and intractability. A guide to the theory of NP-completeness. W.H. Freeman and Company, San Francisco (1979)
Graham, R.L., Lawler, E.L., Lenstra, J.K., Rinnooy Kan, A.H.G.: Optimization and approximation in deterministic sequencing and scheduling: A survey. Ann Discrete Math 5, 287–326 (1979)
Herrbach, L.A., Leung, J.Y.-T.: Preemptive scheduling of equal length jobs on two machines to minimize mean flow time. Operations Research 38, 487–494 (1990)
Kravchenko, S.A.: On the complexity of minimizing the number of late jobs in unit time open shop. Discrete Applied Mathematics 100, 127–132 (2000)
Leung, J.Y.-T., Young, G.H.: Preemptive scheduling to minimize mean weighted flow time. Information Processing Letters 34, 47–50 (1990)
Lawler, E.L.: Combinatorial Optimization: Networks and Matroids. Holt, Rinehart and Winston, New York (1976)
McNaughton, R.: Scheduling with deadlines and loss functions. Management Science 6, 1–12 (1959/1960)
Mokotoff, E.: Parallel machine scheduling problem: survey. Asia-Pacific Journal of Operational Research 18, 193–242 (2001)
Schrijver, A.: Combinatorial Optimization. Springer, Berlin (2003)
Tautenhahn, T., Woeginger, G.J.: Minimizing the total completion time in a unittime open shop with release times. Operations Research Letters 20, 207–212 (1997)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Brucker, P., Kravchenko, S.A. (2005). Polynomial Algorithm for Parallel Machine Mean Flow Time Scheduling Problem with Release Dates. In: Gervasi, O., et al. Computational Science and Its Applications – ICCSA 2005. ICCSA 2005. Lecture Notes in Computer Science, vol 3483. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11424925_21
Download citation
DOI: https://doi.org/10.1007/11424925_21
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-25863-6
Online ISBN: 978-3-540-32309-9
eBook Packages: Computer ScienceComputer Science (R0)