Advertisement

A Branch and Bound Algorithm for the Job Shop Scheduling Problem

  • Jacek Błażewicz
  • Erwin Pesch
  • Małgorzata Sterna

Abstract

The work is concerned with the deterministic case of the non-preemptive job shop scheduling problem. The presented approach is based on the problem representation in the form of a modified disjunctive graph extended by additional arcs. These modifications resulted from the analysis of time dependencies between feasible starting times of tasks. This technique makes it possible to enlarge a partial solution during the search for the optimal tasks’ sequence and it is used as a part of a branch and bound algorithm solving the considered problem.

Keywords

Longe Path Conflict Task Distance Analysis Schedule Length Disjunctive Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Adams J., Balas E., Zawack D. (1988), The shifting bottleneck procedure for job shop scheduling, Management Science, Vol. 34, pp. 391–401CrossRefGoogle Scholar
  2. [2]
    Applegate D., Cook W. (1991), A computational study of the job shop scheduling problem, ORSA Journal of Computing, Vol. 3, pp. 149–156CrossRefGoogle Scholar
  3. [3]
    Balas E., Vazacopoulos A. (1994), Guided Local Search with Shifting Bottleneck for Job Shop Scheduling, Management Science Research Report #MSRR-609, Graduate School of Industrial Administration, Carnegie Melon University, Pittsburgh PA.Google Scholar
  4. [4]
    Bertier P., Roy B., (1965), Trois exemples numeriques d’application de la procedure SEP, Note de travaile n°32 de la Direction Scientifique de la SEMAGoogle Scholar
  5. [5]
    Blazewicz J.,Ecker K.,Pesch E.,Schmidt G., Weglarz J. (1996), Scheduling Computer and Manufacturing Processes, Heidelberg, SpringerCrossRefGoogle Scholar
  6. [6]
    Brucker P., Jurisch B., Sievers B. (1994), A branch and bound algorithm for the job shop scheduling problem, Discrete Applied Mathematics, Vol. 49, pp. 107–127CrossRefGoogle Scholar
  7. [7]
    Carlier J., Pinson E. (1989), An algorithm for solving the job-shop problem, Management Science, Vol. 35, pp. 164–176CrossRefGoogle Scholar
  8. [8]
    Carlier J., Pinson E. (1994), Adjustment of heads and tails for the job-shop problem, European Journal of Operational Research, Vol. 78, pp. 146–161CrossRefGoogle Scholar
  9. [9]
    Caseau Y., Laburthe F. (1995), Disjunctive Scheduling with Task Intervals, Laboratoire d’Informatique de l’Ecole Normale Supérieure, Liens-95–25, ParisGoogle Scholar
  10. [10]
    Ching-Chih Han, Chia-Hoang Lee (1988), Comments on Mohr and Henderson’s path consistency algorithm, Artificial Intelligence, Vol. 36, pp. 125–130CrossRefGoogle Scholar
  11. [11]
    Deo N. (1974), Graph Theory with Applications to Engineering and Computer Science, Englewood Cliffs, Prentice Hall Inc.Google Scholar
  12. [12]
    Fisher H., Thompson G.L. (1963), Probabilistic learning combinations of local job-shop scheduling rules, In: ( Muth J.F., Thompson G. eds.)–Industrial Scheduling, Englewood Cliffs, Prentice Hall, pp. 225–251Google Scholar
  13. [13]
    Floyd R.W. (1962), Algorithm 97: shortest path, Communications ACM, Vol. 5, pp. 345CrossRefGoogle Scholar
  14. [14]
    Garey M.R., Johnson D.S. (1979), Computers and Intractability, San Francisco, Freeman and CompanyGoogle Scholar
  15. [15]
    Hefetz H., Aidiri I. (1982), An efficient optimal algorithm for two-machine unit-time job shop schedule length problem, Mathematics of Operations Research, Vol. 7, pp. 354–360CrossRefGoogle Scholar
  16. [16]
    Jackson J. R. (1965), An extension of Johnson’s results on job shop scheduling, Naval Research Logistic Quarterly, Vol. 3, pp. 201–203CrossRefGoogle Scholar
  17. [17]
    Laarhoven P.J.M., Aarts E.H.L., Lenstra J.K. (1992), Job shop scheduling by simulated annealing, Operations Research, Vol. 40, pp. 113–125CrossRefGoogle Scholar
  18. [18]
    Lawrence S. (1984), Resource constrained project scheduling: an experimental investigation of heuristic scheduling techniques (Supplement), Graduate School of Industrial Administration, Carnegie-Mellon University, Pittsburgh, PennsylvaniaGoogle Scholar
  19. [19]
    Lenstra J.K.,Rinnooy Kan A.H.G. (1979), Computational complexity of discrete optimization problems, Annals of Discrete Mathematics, Vol. 4, pp. 121–140CrossRefGoogle Scholar
  20. [20]
    Mcmahon G., Florian M. (1975), On scheduling with ready times and due dates to minimize maximum lateness, Operations Research, Vol. 23, pp. 475–482CrossRefGoogle Scholar
  21. [21]
    Mohr R., Henderson T.C. (1986), Arc and path consistency revisited, Artificial Intelligence, Vol. 28, pp. 225–233CrossRefGoogle Scholar
  22. [22]
    Nowicki E., Smutnicki C. (1996), A fast taboo search algorithm for the job-shop problem, Management Science, Vol. 46, pp. 797–813CrossRefGoogle Scholar
  23. [23]
    Pesch E., (1994), Learning in Automated Manufacturing. A Local Search Approach, Heidelberg, PhysicaCrossRefGoogle Scholar
  24. [24]
    Rinnooy Kan A.H.G. (1976), Machine Scheduling Problems: Classification, Complexity and Computations, The Hague, NijhoffGoogle Scholar
  25. [25]
    Roy B., Sussmann B. (1964), Les problémes d’ordonnancement avec constraintes disjoncties, SEMA, Note D.S., No 9, ParisGoogle Scholar
  26. [26]
    Storer R.H., Wu S.D, Vaccari R. (1992), New search spaces for sequencing instances with application to job shop scheduling, Management Science, Vol. 38, pp. 1495–1509CrossRefGoogle Scholar
  27. [27]
    Widmer M. (1989), Job-shop scheduling with tooling constraints: a tabu search approach, OR working paper 89/22, Départment of Mathématiques, Ecole Polytechnique Fédérale de LausanneGoogle Scholar
  28. [28]
    Yamada T., Nakano R. (1992), A genetic algorithm applicable to large-scale job-shop problems, In: ( Männer R., Manderick B. eds.) Parallel Problem Solving from Nature 2, Amsterdam, Elsevier Publisher, pp. 281–290Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Jacek Błażewicz
    • 1
  • Erwin Pesch
    • 2
  • Małgorzata Sterna
    • 1
  1. 1.Institute of Computing SciencePoznań University of TechnologyPoland
  2. 2.Institute of Economics and Business Administration, BWL 3University of BonnGermany

Personalised recommendations