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Scheduling jobs in open shops with limited machine availability

Published online by Cambridge University Press:  15 December 2002

Jacek Błażewicz  and
Piotr Formanowicz
Jacek Błażewicz
Affiliation:
Institute of Computing Science, Poznań University of Technology, Piotrowo 3A, 60-965 Poznań, Poland and Institute of Bioorganic Chemistry, Polish Academy of Sciences, Noskowskiego 12/14, 61-704 Poznań, Poland; Piotr.Formanowicz@cs.put.poznan.pl.
Piotr Formanowicz
Affiliation:
Institute of Computing Science, Poznań University of Technology, Piotrowo 3A, 60-965 Poznań, Poland and Institute of Bioorganic Chemistry, Polish Academy of Sciences, Noskowskiego 12/14, 61-704 Poznań, Poland; Piotr.Formanowicz@cs.put.poznan.pl.
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Abstract

In this paper, open shop scheduling problems with limited machine availability are studied. Such a limited availability of machines may appear in many real-life situations, e.g. as preventive maintenance activities. Three types of jobs are distinguished: non-preemptable, resumable and preemptable. An operation of a resumable job if not completed before a non-availability period of a machine may be suspended and continued without additional cost when the machine becomes available. In the paper, results are given for the scheduling problems associated with the three types of jobs. For preemptable jobs polynomial-time algorithms based on the two-phase method are proposed.

Keywords

Limited machine availabilitycomputational complexitytwo-phase methodmathematical programming.
Type
Research Article
Information
RAIRO - Operations Research , Volume 36 , Issue 2 , April 2002 , pp. 149 - 156
Copyright
© EDP Sciences, 2002

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References

Błazewicz, J., Breit, J., Formanowicz, P., Kubiak, W. and Schmidt, G., Heuristic algorithms for the two-machine flowshop with limited machine availability. Omega - International J. Management Sci. 29 (2001) 599-608. CrossRef
Błazewicz, J., Drozdowski, M., Formanowicz, P., Kubiak, W. and Schmidt, G., Scheduling preemtable tasks on parallel processors with limited availability. Parallel Comput. 26 (2000) 1195-1211. CrossRef
J. Błazewicz, K. Ecker, E. Pesch, G. Schmidt and J. Weglarz, Scheduling Computer and Manufacturing Processes, 2nd Edition. Springer-Verlag, Berlin (2001).
Dolev, D. and Warmuth, M.K., Profile scheduling of opposing forests and level orders. SIAM J. Algebraic Discrete Meth. 6 (1985) 665-687. CrossRef
Dolev, D. and Warmuth, M., Scheduling flat graphs. SIAM J. Comput. 14 (1985) 638-657. CrossRef
P. Formanowicz, Scheduling jobs in systems with limited availability of processors (in Polish), Ph.D. Thesis. Institute of Computing Science, Poznan University of Technology, Poznan (2000).
Formanowicz, P., Selected deterministic scheduling problems with limited machine availability. Pro Dialog 13 (2001) 91-105.
M.R. Garey and D.S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness. W.H. Freeman, San Francisco (1979).
Garey, M.R., Johnson, D.S., Tarjan, R.E. and Yannakakis, M., Scheduling opposing forests. SIAM J. Alg. Disc. Meth. 4 (1983) 72-93. CrossRef
Kubiak, W., Błazewicz, J., Formanowicz, P., Breit, J. and Schmidt, G., Two-machine flow shops with limited machine availability. Eur. J. Oper. Res. 136 (2002) 528-540. CrossRef
Lee, C.-Y., Machine scheduling with an availability constraint. J. Global Optim. 9 (1996) 395-416. CrossRef
Lee, C.-Y., Minimizing the makespan in the two-machine flow shop scheduling problem with an availability constraint. Oper. Res. Lett. 20 (1997) 129-139. CrossRef
Lee, C.-Y., Two-machine flowshop scheduling with availability constraints. Eur. J. Oper. Res. 114 (1999) 420-429. CrossRef
Liu, Z. and Sanlaville, E., Preemptive scheduling with variable profile, precedence constraints and due dates. Discrete Appl. Math. 58 (1995) 253-280. CrossRef
Sanlaville, E. and Schmidt, G., Machine scheduling with availability constraints. Acta Informatica 35 (1998) 795-811. CrossRef
Schmidt, G., Scheduling on semi-identical processors. Z. Oper. Res. A 28 (1984) 153-162.
Schmidt, G., Scheduling independent tasks with deadlines on semi-identical processors. J. Oper. Res. Soc. 39 (1988) 271-277. CrossRef
Schmidt, G., Scheduling with limited machine availability. Eur. J. Oper. Res. 121 (2000) 1-15. CrossRef