no. 2
Scheduling jobs in open shops with limited machine availability
RAIRO - Operations Research - Recherche Opérationnelle, Tome 36 (2002) no. 2, pp. 149-156.

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.

DOI : 10.1051/ro:2002008
Mots clés : limited machine availability, computational complexity, two-phase method, mathematical programming 
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Błażewicz, Jacek; Formanowicz, Piotr. Scheduling jobs in open shops with limited machine availability. RAIRO - Operations Research - Recherche Opérationnelle, Tome 36 (2002) no. 2, pp. 149-156. doi : 10.1051/ro:2002008. http://www.numdam.org/articles/10.1051/ro:2002008/

[1] J. Błażewicz, J. Breit, P. Formanowicz, W. Kubiak and G. Schmidt, Heuristic algorithms for the two-machine flowshop with limited machine availability. Omega - International J. Management Sci. 29 (2001) 599-608.

[2] J. Błażewicz, M. Drozdowski, P. Formanowicz, W. Kubiak and G. Schmidt, Scheduling preemtable tasks on parallel processors with limited availability. Parallel Comput. 26 (2000) 1195-1211. | Zbl

[3] J. Błażewicz, K. Ecker, E. Pesch, G. Schmidt and J. Wȩglarz, Scheduling Computer and Manufacturing Processes, 2nd Edition. Springer-Verlag, Berlin (2001). | Zbl

[4] D. Dolev and M.K. Warmuth, Profile scheduling of opposing forests and level orders. SIAM J. Algebraic Discrete Meth. 6 (1985) 665-687. | MR | Zbl

[5] D. Dolev and M. Warmuth, Scheduling flat graphs. SIAM J. Comput. 14 (1985) 638-657. | MR | Zbl

[6] P. Formanowicz, Scheduling jobs in systems with limited availability of processors (in Polish), Ph.D. Thesis. Institute of Computing Science, Poznań University of Technology, Poznań (2000).

[7] P. Formanowicz, Selected deterministic scheduling problems with limited machine availability. Pro Dialog 13 (2001) 91-105.

[8] M.R. Garey and D.S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness. W.H. Freeman, San Francisco (1979). | MR | Zbl

[9] M.R. Garey, D.S. Johnson, R.E. Tarjan and M. Yannakakis, Scheduling opposing forests. SIAM J. Alg. Disc. Meth. 4 (1983) 72-93. | MR | Zbl

[10] W. Kubiak, J. Błażewicz, P. Formanowicz, J. Breit and G. Schmidt, Two-machine flow shops with limited machine availability. Eur. J. Oper. Res. 136 (2002) 528-540. | Zbl

[11] C.-Y. Lee, Machine scheduling with an availability constraint. J. Global Optim. 9 (1996) 395-416. | MR | Zbl

[12] C.-Y. Lee, Minimizing the makespan in the two-machine flow shop scheduling problem with an availability constraint. Oper. Res. Lett. 20 (1997) 129-139. | MR | Zbl

[13] C.-Y. Lee, Two-machine flowshop scheduling with availability constraints. Eur. J. Oper. Res. 114 (1999) 420-429. | Zbl

[14] Z. Liu and E. Sanlaville, Preemptive scheduling with variable profile, precedence constraints and due dates. Discrete Appl. Math. 58 (1995) 253-280. | MR | Zbl

[15] E. Sanlaville and G. Schmidt, Machine scheduling with availability constraints. Acta Informatica 35 (1998) 795-811. | MR | Zbl

[16] G. Schmidt, Scheduling on semi-identical processors. Z. Oper. Res. A 28 (1984) 153-162. | MR | Zbl

[17] G. Schmidt, Scheduling independent tasks with deadlines on semi-identical processors. J. Oper. Res. Soc. 39 (1988) 271-277. | Zbl

[18] G. Schmidt, Scheduling with limited machine availability. Eur. J. Oper. Res. 121 (2000) 1-15. | MR | Zbl

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