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)


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


Jobshop scheduling branch and bound heuristics propagation constraints 


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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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