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New MIP model for Multiprocessor Scheduling Problem with Communication Delays

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Book cover Open Problems in Optimization and Data Analysis

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 141))

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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.

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Acknowledgements

The authors would like to gratefully thank the IRT (Institut de recherche technologique) Railenium for the financial support to achieve this research. Also, the authors thank the International Chair Professor N. Mladenović, for his contribution to this work. This Chair position at the University of Valenciennes is cofunded by the region Nord-Pas-de-Calais and the IRT Railenium. This research is conducted within or partially covered by the framework of the grant num. BR05236839 “Development of information technologies and systems for stimulation of personality’s sustainable development as one of the bases of development of digital Kazakhstan”.

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Authors and Affiliations

  1. Université Polytechnique Hauts-De-France (UPHF)/LAMIH CNRS UMR 8201, Campus Mont-Houy, Valenciennes Cedex 9, France

    Abdessamad Ait El Cadi & Mustapha Ratli

  2. Emirates College of Technologies, Abu Dhabi, UAE

    Nenad Mladenović

  3. Mathematical Institute, SASA, Belgrade, Serbia

    Nenad Mladenović

Authors
  1. Abdessamad Ait El Cadi
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  2. Mustapha Ratli
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  3. Nenad Mladenović
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Corresponding author

Correspondence to Abdessamad Ait El Cadi .

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Editors and Affiliations

  1. Industrial and Systems, Engineering Department, University of Florida, Center For Applied Optimization, Gainesville, FL, USA

    Panos M. Pardalos

  2. Industrial Logistics, ETS Institute, Lulea University of Technology, Norrbotten, Sweden

    Athanasios Migdalas

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Ait El Cadi, A., Ratli, M., Mladenović, N. (2018). New MIP model for Multiprocessor Scheduling Problem with Communication Delays. In: Pardalos, P., Migdalas, A. (eds) Open Problems in Optimization and Data Analysis. Springer Optimization and Its Applications, vol 141. Springer, Cham. https://doi.org/10.1007/978-3-319-99142-9_8

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