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Improving branch and bound for Jobshop scheduling with constraint propagation

  • Yves Caseau
  • François Laburthe
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1120)

Abstract

Task intervals were defined in [CL94] for disjunctive scheduling so that, in a scheduling problem, one could derive much information by focusing on some key subsets of tasks. The advantage of this approach was to shorten the size of search trees for branch&bound algorithms because more propagation was performed at each node.

In this paper, we refine the propagation scheme and describe in detail the branch&bound algorithm with its heuristics and we compare constraint programming to integer programming. This algorithm is tested on the standard benchmarks from Muth & Thompson, Lawrence, Adams et al, Applegate & Cook and Nakano & Yamada. The achievements are the following:
  • Window reduction by propagation: for 23 of the 40 problems of Lawrence, the proof of optimality is found with no search, by sole propagation; for typically hard 10×10 problems, the search tree has less than a thousand nodes; hard problems with up to 400 tasks can be solved to optimality and among these, the open problem LA21 is solved within a day.

  • Lower bounds very quick to compute and which outperform by far lower bounds given by cutting planes. The lower bound to the open 20×20 problem YAM1 is improved from 812 to 826

keywords

Jobshop scheduling branch and bound heuristics propagation constraints 

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References

  1. [ABZ88]
    J.Adams, E. Balas & D. Zawak. The Shifting Bottleneck Procedure for Job Shop Scheduling. Management Science 34, p391–401. 1988Google Scholar
  2. [AC91]
    D. Applegate & B. Cook. A Computational Study of the Job Shop Scheduling Problem. Operations Research Society of America 3, 1991Google Scholar
  3. [Ba 69]
    E. Balas. Machine Sequencing via Disjunctive Programming: an Implicit Enumeration Algorithm. Operations Research 17, p 941–957. 1969Google Scholar
  4. [Ba 85]
    E. Balas On the facial structure of Scheduling Polyhedra, Mathematical Programming studies 24, p. 179–218.Google Scholar
  5. [BL 95]
    P. Baptiste, C. Le Pape A theoretical and experimental comparison of constraint propagation techniques for disjunctive scheduling. Proc. of the 14th International Joint Conference on Artificila Intellignece, 1995.Google Scholar
  6. [Ca 82]
    J. Carlier. The one machine sequencing problem European Journal of Operations Research 11, p. 42–47, 1982.Google Scholar
  7. [CP89]
    J. Carlier & E. Pinson. An Algorithm for Solving the Job Shop Problem. Management science, vol 35, no 2, february 1989Google Scholar
  8. [CP94]
    J. Carlier & E. Pinson. Adjustments of heads and tails for the job-shop problem, European Journal of Operations Research, vol 78, 1994, p. 146–161.CrossRefGoogle Scholar
  9. [Ca 91]
    Y. Caseau. A Deductive Object-Oriented Language. Annals of Maths and Artificial Intelligence, Special Issue on Deductive Databases, March 1991.Google Scholar
  10. [CGL93]
    Y. Caseau, P.-Y. Guillo & E. Levenez. A Deductive and Object-Oriented Approach to a Complex Scheduling Problem. Proc. of DOOD'93, 1993Google Scholar
  11. [CK92]
    Y. Caseau & P. Koppstein. A Cooperative-Architecture Expert System for Solving Large Time/Travel Assignment Problems. International Conference on Databases and Expert Systems Applications, Spain, 1992.Google Scholar
  12. [CL94]
    Y. Caseau & F. Laburthe. Improved CLP Scheduling with Task Intervals. Proc. of the Eleventh International Conference on Logic Programming, ed: P. van Hentenryck, The MIT Press, 1994.Google Scholar
  13. [CL95]
    Y. Caseau & F. Laburthe. Disjunctive Scheduling with Task Intervals. LIENS report 95-25, École Normale Supérieure, 1995.Google Scholar
  14. [DP95]
    L. Djerid & M.-C. Portmann. Comment entrecroiser des procédures par séparation et évaluation et des algorithmes génétiques: application à des problèmes d'ordonnancement à contraintes disjunctives. FRANCORO, Mons, 1995, p. 84–85Google Scholar
  15. [DT93]
    M. Dell'Amico & M. Trubian. Applying Tabu-Search to the Job-Shop Scheduling Problem. Annals of Operations Research, vol 41, 1993, p. 231–252Google Scholar
  16. [DW90]
    M. Dyer & L.A. Wolsey. Formulating the Single Machine Sequencing Problem with Release Dates as a Mixed Integer Program. Discrete Applied Mathematics 26, p.255–270. 1990.CrossRefGoogle Scholar
  17. [La84]
    S. Lawrence. Resource Constrained Project Scheduling: an Experimental Investigation of Heuristic Scheduling Techniques. GSIA, C.M.U. 1984Google Scholar
  18. [MT63]
    J.F. Muth & G.L. Thompson Industrial scheduling. Prentice Hall, 1963.Google Scholar
  19. [NY92]
    Nakano & Yamada A Genetic Algorithm applicable to Large Scale JobShop Problems. Parallel Problem solving from Nature 2, Elsevier, 1992.Google Scholar
  20. [Ta89]
    E. Taillard. Parallel Taboo Search Technique for the Jobshop Scheduling Problem. Internal Report ORPWP 89/11, École Polytechnique Fédérale de Lausanne, 1989Google Scholar
  21. [VH89]
    P. Van Hentenryck. Constraint Satisfaction in Logic Programming. The MIT press, Cambridge, 1989.Google Scholar
  22. [VDV91]
    S.L. Van De Velde. Machine scheduling and Lagrangian relaxation. Doctoral Thesis, CWI, Amsterdam, 1991Google Scholar
  23. [VLA92]
    P van Laarhoven, E.Aarts & J.K. Lenstra. Job Shop Scheduling by Simulated Annealing. Operations Research vol 40, no 1, 1992Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Yves Caseau
    • 1
  • François Laburthe
    • 2
  1. 1.Bouygues-Direction ScientifiqueSt Quentin en YvelinesFrance
  2. 2.Ecole Normale SupérieureD.M.I.ParisFrance

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