A Constraint Integer Programming Approach for Resource-Constrained Project Scheduling

  • Timo Berthold
  • Stefan Heinz
  • Marco E. Lübbecke
  • Rolf H. Möhring
  • Jens Schulz
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6140)


We propose a hybrid approach for solving the resource-constrained project scheduling problem which is an extremely hard to solve combinatorial optimization problem of practical relevance. Jobs have to be scheduled on (renewable) resources subject to precedence constraints such that the resource capacities are never exceeded and the latest completion time of all jobs is minimized.

The problem has challenged researchers from different communities, such as integer programming (IP), constraint programming (CP), and satisfiability testing (SAT). Still, there are instances with 60 jobs which have not been solved for many years. The currently best known approach, lazyFD, is a hybrid between CP and SAT techniques.

In this paper we propose an even stronger hybridization by integrating all the three areas, IP, CP, and SAT, into a single branch-and-bound scheme. We show that lower bounds from the linear relaxation of the IP formulation and conflict analysis are key ingredients for pruning the search tree. First computational experiments show very promising results. For five instances of the well-known PSPLib we report an improvement of lower bounds. Our implementation is generic, thus it can be potentially applied to similar problems as well.


Constraint Programming Precedence Constraint Project Schedule Linear Programming Relaxation Linear Relaxation 
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.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Timo Berthold
    • 1
  • Stefan Heinz
    • 1
  • Marco E. Lübbecke
    • 2
  • Rolf H. Möhring
    • 3
  • Jens Schulz
    • 3
  1. 1.Zuse Institute BerlinBerlinGermany
  2. 2.Fachbereich MathematikTechnische Universität DarmstadtDarmstadtGermany
  3. 3.Institut für MathematikTechnische Universität BerlinBerlinGermany

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