An efficient ILP formulation for the single machine scheduling problem

Cyril Briand; Samia Ourari; Brahim Bouzouia

RAIRO - Operations Research (2010)

  • Volume: 44, Issue: 1, page 61-71
  • ISSN: 0399-0559

Abstract

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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 (Lmax). Experiments have been performed by means of a commercial solver that show that this formulation is effective on large problem instances. A comparison with the branch-and-bound procedure of Carlier is provided.

How to cite

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Briand, Cyril, Ourari, Samia, and Bouzouia, Brahim. "An efficient ILP formulation for the single machine scheduling problem." RAIRO - Operations Research 44.1 (2010): 61-71. <http://eudml.org/doc/250835>.

@article{Briand2010,
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 (Lmax). Experiments have been performed by means of a commercial solver that show that this formulation is effective on large problem instances. A comparison with the branch-and-bound procedure of Carlier is provided. },
author = {Briand, Cyril, Ourari, Samia, Bouzouia, Brahim},
journal = {RAIRO - Operations Research},
keywords = {Single machine scheduling; integer linear programming; dominance conditions; single machine scheduling},
language = {eng},
month = {2},
number = {1},
pages = {61-71},
publisher = {EDP Sciences},
title = {An efficient ILP formulation for the single machine scheduling problem},
url = {http://eudml.org/doc/250835},
volume = {44},
year = {2010},
}

TY - JOUR
AU - Briand, Cyril
AU - Ourari, Samia
AU - Bouzouia, Brahim
TI - An efficient ILP formulation for the single machine scheduling problem
JO - RAIRO - Operations Research
DA - 2010/2//
PB - EDP Sciences
VL - 44
IS - 1
SP - 61
EP - 71
AB - 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 (Lmax). Experiments have been performed by means of a commercial solver that show that this formulation is effective on large problem instances. A comparison with the branch-and-bound procedure of Carlier is provided.
LA - eng
KW - Single machine scheduling; integer linear programming; dominance conditions; single machine scheduling
UR - http://eudml.org/doc/250835
ER -

References

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  1. 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.  
  2. J. Carlier, The one-machine sequencing problem. Eur. J. Oper. Res.11 (1982) 42–47.  Zbl0482.90045
  3. J. Erschler, F. Roubellat and J.-P Vernhes, 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.  Zbl0425.90053
  4. J. Erschler, G. Fontan, C. Merce and F. Roubellat, A New Dominance Concept in Scheduling n Jobs on a Single Machine with Ready Times and Due Dates. Oper. Res.31 (1983) 114–127.  Zbl0495.90046
  5. A.M. Hariri and C.N. Potts, An algorithm for single machine sequencing with release dates to minimize total weighted completion time. Discrete Appl. Math.5 (1983) 99–109.  Zbl0498.90044
  6. J.K. Lenstra, A.H.G. Rinnooy Han and P. Brucker, Complexity of machine scheduling problems. Ann. Discrete Math.1 (1977) 343–362.  

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