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An efficient ILP formulation for the single machine scheduling problem

Published online by Cambridge University Press:  08 February 2010

Cyril Briand ,
Samia Ourari  and
Brahim Bouzouia
Cyril Briand
Affiliation:
CNRS, LAAS, 7 avenue du colonel Roche, 31077 Toulouse, France; briand@laas.fr Université de Toulouse, UPS, INSA, INP, ISAE, LAAS, 31077 Toulouse, France; sourari@cdta.dz
Samia Ourari
Affiliation:
CNRS, LAAS, 7 avenue du colonel Roche, 31077 Toulouse, France; briand@laas.fr Université de Toulouse, UPS, INSA, INP, ISAE, LAAS, 31077 Toulouse, France; sourari@cdta.dz CDTA, lotissement du 20 août 1956, Baba Hassen, Alger, Algeria; bbouzouia@cdta.dz
Brahim Bouzouia
Affiliation:
CDTA, lotissement du 20 août 1956, Baba Hassen, Alger, Algeria; bbouzouia@cdta.dz
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Abstract

This paper considers the problem of scheduling n jobs on a single machine. A fixed processing time and an execution interval are associated with each job. Preemption is not allowed. On the basis of analytical and numerical dominance conditions, an efficient integer linear programming formulation is proposed for this problem, aiming at minimizing the maximum lateness (L max). Experiments have been performed by means of a commercial solver that show that this formulation iseffective on large problem instances. A comparison with thebranch-and-bound procedure of Carlier is provided.

Keywords

Single machine schedulinginteger linear programmingdominance conditions
Type
Research Article
Information
RAIRO - Operations Research , Volume 44 , Issue 1 , January 2010 , pp. 61 - 71
Copyright
© EDP Sciences, ROADEF, SMAI, 2010

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References

C. Briand, H.T. La and J. Erschler, Une approche pour l'ordonnancement robuste de tâches sur une machine, 4ème Conférence Francophone de MOdélisation et SIMulation (MOSIM'03). Toulouse, France (2003) 205–211.
Carlier, J., The one-machine sequencing problem. Eur. J. Oper. Res. 11 (1982) 42–47. CrossRef
Erschler, J., Roubellat, F. and Vernhes, J.-P, Characterizing the set of feasible sequences for n jobs to be carried out on a single machine. Eur. J. Oper. Res. 4 (1980) 189–194. CrossRef
Erschler, J., Fontan, G., Merce, C. and Roubellat, F., New Dominance Concept, A in Scheduling n Jobs on a Single Machine with Ready Times and Due Dates. Oper. Res. 31 (1983) 114–127. CrossRef
Hariri, A.M. and Potts, C.N., An algorithm for single machine sequencing with release dates to minimize total weighted completion time. Discrete Appl. Math. 5 (1983) 99–109. CrossRef
Lenstra, J.K., Rinnooy Han, A.H.G. and Brucker, P., Complexity of machine scheduling problems. Ann. Discrete Math. 1 (1977) 343–362. CrossRef