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Evaluating flexible solutions in single machine scheduling via objective function maximization: the study of computational complexity

Published online by Cambridge University Press:  15 June 2007

Mohamed Ali Aloulou ,
Mikhail Y. Kovalyov  and
Marie-Claude Portmann
Mohamed Ali Aloulou
Affiliation:
LAMSADE – Université Paris Dauphine, Place du Maréchal de Lattre de Tassigny, 75775 Paris Cedex 16, France; aloulou@lamsade.dauphine.fr
Mikhail Y. Kovalyov
Affiliation:
Faculty of Economics, Belarusian State University, and United Institute of Informatics Problems, National Academy of Sciences of Belarus, Minsk, Belarus; koval@newman.bas-net.by
Marie-Claude Portmann
Affiliation:
MACSI team of INRIA-Lorraine and LORIA-INPL, École des Mines de Nancy, Parc de Saurupt, 54042 Nancy Cedex, France; portmann@loria.fr
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Abstract

We study a deterministic problem of evaluating the worst case performance of flexible solutions in the single machine scheduling. A flexible solution is a set of schedules following a given structure determined by a partial order of jobs and a type of the schedules. In this paper, the schedules of active and non-delay type are considered. A flexible solution can be used on-line to absorb the impact of data disturbances related to, for example, job arrival, tool availability or machine breakdowns. The performance of a flexible solution includes the best case and the worst case performances. The best case performance is an ideal performance that can be achieved only if the on-line conditions allow to implement the best schedule of the set of schedules characterizing the flexible solution. In contrast, the worst case performance indicates how poorly the flexible solution may perform when following the given structure in the on-line circumstances. The best-case and the worst-case performances are usually evaluated by the minimum and maximum values of the considered objective function, respectively. We present algorithmic and computational complexity results for some maximization scheduling problems. In these problems, the jobs to be scheduled have different release dates and precedence constraints may be given on the set of jobs.

Keywords

Schedulingsingle machineschedule flexibilitymaximization problemsactive and non-delay schedules.
Type
Research Article
Information
RAIRO - Operations Research , Volume 41 , Issue 1 , January 2007 , pp. 1 - 18
Copyright
© EDP Sciences, ROADEF, SMAI, 2007

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References

M.A. Aloulou, On the reactive scheduling design using flexible predictive schedules, in Proceedings of IEEE SMC'2002, 6 pages in CD–ROM, Hammamet, October 2002.
Aloulou, M.A., Kovalyov, M.Y. and Portmann, M.C., Maximization problems in single machine scheduling. Ann. Oper. Res. 129 (2004) 21–35. CrossRef
M.A. Aloulou and M.C. Portmann, An efficient proactive reactive approach to hedge against shop flow disruptions, in Multidisciplinary Scheduling: Thoery and Applications, edited by G. Kendall, E. Burke, S. Petrovic and M. Gendreau, Springer (2005) 223–246.
Artigues, C., Billaut, J.-C. and Esswein, C., Maximization of solution flexibility for robust shop scheduling. Eur. J. Oper. Res. 165 (2005) 314–328. CrossRef
Artigues, C., Roubellat, F. and Billaut, J.-C., Characterization of a set of schedules in a resource constrained multi-project scheduling problem with multiple modes. Inter. J. Industrial Eng. Applications Practice 6 (1999) 112–122.
K.R. Baker, Introduction to sequencing and scheduling. John Wiley and Sons (1974).
P. Brucker, Scheduling algorithms. Springer-Verlag (1998).
P. Brucker and S. Knust, Complexity results for scheduling problems. http://www.mathematik.uni-osnabrueck.de/research/OR/class/ (2003).
Daniels, R.L. and Kouvelis, P., Robust scheduling to hedge against processing time uncertainty in single stage production. Manage. Sci. 41 (1995) 363–376. CrossRef
M.R. Garey and D.S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness, edited by W.H. Freeman (1979).
Graham, R.L., Lawler, E.L., Lenstra, J.K. and Rinnooy Kan, A.H.G., Optimization and approximation in deterministic machine scheduling: a survey. Ann. Discrete Math. 5 (1979) 287–326. CrossRef
Herroelen, W. and Leus, R., Project scheduling under uncertainty: survey and research potentials. Eur. J. Oper. Res. 165 (2005) 289–306. CrossRef
E.L. Lawler, Scheduling a single machine to minimize the number of late jobs. Technical report, Computer Science Division, University of California, Berkeley, USA (1983).
Mehta, S.V. and Uzsoy, R., Predictable scheduling of a single machine subject to breakdowns. Inter. J. Compu. Integrated Manufacturing 12 (1999) 15–38. CrossRef
M.E. Posner, Reducibility among weighted completion time scheduling problems. Ann. Oper. Res. (1990) 91–101.
Smith, W.E., Various optimizers for single-stage production. Naval Research Logistics Quarterly 3 (1956) 59–66. CrossRef
V.S. Tanaev, V.S. Gordon and Y.M. Shafransky, Scheduling Theory. Single-Stage Systems. Kluwer Academic Publishers (1994).
Wu, S.D., Byeon, E.S. and Storer, R.H., A graph-theoretic decomposition of the job shop scheduling problem to achieve scheduling robustness. Oper. Res. 47 (1999) 113–124. CrossRef