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Scheduling with periodic availability constraints and irregular cost functions

Published online by Cambridge University Press:  15 June 2007

Francis Sourd
Francis Sourd*
Affiliation:
CNRS-LIP6. 4, place Jussieu 75252 Paris Cedex 05, France; [email protected]
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Abstract

This paper addresses a one-machine scheduling problem in which the efficiency of the machine is not constant, that is the duration of a task is longer in badly efficient time periods. Each task has an irregular completion cost. Under the assumption that the efficiency constraints are time-periodic, we show that the special case where the sequence is fixed can be solved in polynomial time. The general case is NP-complete so that we propose a two-phase heuristic to find good solutions. Our approach is tested on problems with earliness-tardiness costs.

Keywords

Schedulingearliness-tardinessavailabilitybreak
Type
Research Article
Information
RAIRO - Operations Research , Volume 41 , Issue 2: ROADEF 05 , April 2007 , pp. 141 - 154
Copyright
© EDP Sciences, ROADEF, SMAI, 2007

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References

Brauner, N., Crama, Y., Grigoriev, A. and van de Klundert, A framework for the complexity of high-multiplicity scheduling problems. J. Combin. Optim. 9 (2005) 313–323. CrossRef
Clifford, J.J. and Posner, M.E., High multiplicity in earliness-tardiness scheduling. Oper. Res. 48 (2000) 788–800. CrossRef
Garey, M.R., Tarjan, R.E. and Wilfong, G.T., One-processor scheduling with symmetric earliness and tardiness penalties. Math. Oper. Res. 13 (1988) 330–348. CrossRef
Grosso, A., Della Croce, F. and Tadei, R., An enhanced dynasearch neighborhood for the single-machine total weighted tardiness scheduling problem. Oper. Res. Lett. 32 (2004) 68–72. CrossRef
C. Hanen and A. Munier, Cyclic scheduling on parallel processors: an overview, Scheduling Theory and its applications, edited by P. Chrétienne, E.G. Coffman, J.K. Lenstra and Z. Liu, John Wiley & Sons (1995) 193–226.
Hendel, Y. and Sourd, F., Efficient neighborhood search for the one-machine ealiness-tardiness scheduling problems. Eur. J. Oper. Res. 173 (2006) 108–119. CrossRef
Hochbaum, D. S. and Shamir, R., Strongly polynomial algorithms for the high multiplicity scheduling problem. Oper. Res. 39 (1991) 648–653. CrossRef
ILOG Inc., ILOG Scheduler 6.0 User's Manual and Reference Manual (October 2003).
C.-Y. Lee, Machine scheduling with availability constraints, Handbook of scheduling: Algorithms, models and performance analysis, edited by J.Y.-T. Leung, Chapman & Hall/CRC (2004).
W. Nuijten, T. Bousonville, F. Focacci, D. Godard and C. Le Pape, Towards a real-life manufacturing scheduling problem and test bed, in Proceedings of PMS'04, http://www2.ilog.com/masclib (2004) 162–165.
Sourd, F., Optimal timing of a sequence of tasks with general completion costs. Eur. J. Oper. Res. 165 (2005) 82–96. CrossRef
F. Sourd and S. Kedad-Sidhoum, A new branch-and-bound algorithm for the minimization of earliness and tardiness on a single machine, in 7th workshop on Models and Algorithms for Planning and Scheduling Problems (2005) 258–261.