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Mathematical Model for Production Plan Optimization—A Case Study of Discrete Event Systems

Author

Listed:
  • Sadok Rezig

    (Laboratoire de Génie Informatique, de Production et de Maintenance (LGIPM), UFR MIM, University of Lorraine, 57000 Metz, France)

  • Wajih Ezzeddine

    (Laboratoire de Génie Informatique, de Production et de Maintenance (LGIPM), UFR MIM, University of Lorraine, 57000 Metz, France)

  • Sadok Turki

    (Laboratoire de Génie Informatique, de Production et de Maintenance (LGIPM), UFR MIM, University of Lorraine, 57000 Metz, France)

  • Nidhal Rezg

    (Laboratoire de Génie Informatique, de Production et de Maintenance (LGIPM), UFR MIM, University of Lorraine, 57000 Metz, France)

Abstract

This paper proposes an optimal scheduling model under production and maintenance constraints for a real case of a discrete event system. The intent was to use the rich mathematical theory and algorithms of optimization in the study of this important class of systems. The current study detailed firstly a new approach for mapping a simulation event relationship graph into a mixed-integer program, with a flexible workshop real case. Several other potential applications of the mathematical model are examined, thanks to the model constraints flexibility characteristics, including a general case of a manufacturing system for optimal resource scheduling, an application on the case of hospital beds’ management. The model extension could be also interesting for other applications like museum systems or the case of big data in complex and social networks.

Suggested Citation

  • Sadok Rezig & Wajih Ezzeddine & Sadok Turki & Nidhal Rezg, 2020. "Mathematical Model for Production Plan Optimization—A Case Study of Discrete Event Systems," Mathematics, MDPI, vol. 8(6), pages 1-16, June.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:6:p:955-:d:370110
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    References listed on IDEAS

    as
    1. Sadok Rezig & Zied Achour & Nidhal Rezg & Mohamed-Ali Kammoun, 2016. "Supervisory control based on minimal cuts and Petri net sub-controllers coordination," International Journal of Systems Science, Taylor & Francis Journals, vol. 47(14), pages 3425-3435, October.
    2. M. Florian & J. K. Lenstra & A. H. G. Rinnooy Kan, 1980. "Deterministic Production Planning: Algorithms and Complexity," Management Science, INFORMS, vol. 26(7), pages 669-679, July.
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    Cited by:

    1. Yuanxiu Teng & Zhiwu Li & Li Yin & Naiqi Wu, 2023. "State-Based Differential Privacy Verification and Enforcement for Probabilistic Automata," Mathematics, MDPI, vol. 11(8), pages 1-21, April.

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