Explicit Modelling of Multiple Intervals in a Constraint Generation Procedure for Multiprocessor Scheduling

  • Emil KarlssonEmail author
  • Elina Rönnberg
Conference paper
Part of the Operations Research Proceedings book series (ORP)


Multiprocessor scheduling is a well studied NP-hard optimisation problem that occurs in variety of forms. The focus of this paper is explicit modelling of multiple task intervals. This work extends a constraint generation procedure previously developed for an avionics scheduling context. We here address a relaxation of the original problem and this relaxation can be considered as multiprocessor scheduling with precedence relations and multiple intervals. The explicit modelling of multiple intervals strengthens the formulation used in the constraint generation procedure and we illustrate the computational effects on an industrial relevant avionics scheduling problem.


Multiprocessor scheduling Multiple intervals Avionics scheduling Constraint generation 



The work is part of a project funded by the Center for Industrial Information Technology (CENIIT) and the work of Emil Karlsson is supported by the Research School in Interdisciplinary Mathematics at Linköping University.


  1. 1.
    Baltz, A., El Ouali, M., Jäger, G., Sauerland, V., & Srivastav, A. (2015). Exact and heuristic algorithms for the travelling salesman problem with multiple time windows and hotel selection. Journal of the Operational Research Society, 66(4), 615–626.CrossRefGoogle Scholar
  2. 2.
    Blikstad, M., Karlsson, E., Lööw, T., & Rönnberg, E. (2017). An optimisation approach for pre-runtime scheduling of tasks and communication in an integrated modular avionic system. Technical report LiTH-MAT-R–2017/03–SE, Linköping University.Google Scholar
  3. 3.
    Christiansen, M., & Fagerholt, K. (2002). Robust ship scheduling with multiple time windows. Naval Research Logistics, 49(6), 611–625.CrossRefGoogle Scholar
  4. 4.
    Pesant, G., Gendreau, M., Potvin, J.-Y., & Rousseau, J.-M. (1999). On the flexibility of constraint programming models: From single to multiple time windows for the traveling salesman problem. European Journal of Operational Research, 117(2), 253–263.CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsLinköping UniversityLinköpingSweden
  2. 2.Saab ABLinköpingSweden

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