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New MIP model for Multiprocessor Scheduling Problem with Communication Delays

In: Open Problems in Optimization and Data Analysis

Author

Listed:
  • Abdessamad Ait El Cadi

    (Université Polytechnique Hauts-De-France (UPHF)/LAMIH CNRS UMR 8201)

  • Mustapha Ratli

    (Université Polytechnique Hauts-De-France (UPHF)/LAMIH CNRS UMR 8201)

  • Nenad Mladenović

    (Emirates College of Technologies
    Mathematical Institute)

Abstract

In this chapter, we consider The Multiprocessor Scheduling Problem with Communication Delays. We propose a new Mixed Integer Program (MIP) formulation for this problem taking into account the precedence constraints and the communication delays—delays that depend on the network and the tasks. The new proposed formulation reduces both the number of variables and the number of constraints, when compared to the best mathematical programming formulations from the literature. We summarize the mathematical formulation in a previous work and, in the present chapter; we added extra results to show the quality of the new model. The aim of the extended tests is to assess the quality of this model from one side and from the other side to show which parameters affect the performance of our model, especially the network architecture, the communication, and the number of task impacts. The results are significant but there are still some open problems to solve.

Suggested Citation

  • Abdessamad Ait El Cadi & Mustapha Ratli & Nenad Mladenović, 2018. "New MIP model for Multiprocessor Scheduling Problem with Communication Delays," Springer Optimization and Its Applications, in: Panos M. Pardalos & Athanasios Migdalas (ed.), Open Problems in Optimization and Data Analysis, pages 129-149, Springer.
    • Handle: RePEc:spr:spochp:978-3-319-99142-9_8
    DOI: 10.1007/978-3-319-99142-9_8
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