Advertisement

A Cost-Criticality Based (Max, +) Optimization Model for Operations Scheduling

  • Karla Quintero
  • Eric Niel
  • José Aguilar
  • Laurent Piétrac
Conference paper

Abstract

The following work proposes a (max, +) optimization model for scheduling batch transfer operations in a flow network by integrating a cost/criticality criterion to prioritize conflicting operations in terms of resource allocation. The case study is a seaport for oil export where real industrial data has been gathered. The work is extendable to flow networks in general and aims at proposing a general, intuitive algebraic modeling framework through which flow transfer operations can be scheduled based on a criterion that integrates the potential costs due to late client service and critical device reliability in order to satisfy a given set of requests through a set of disjoint alignments in a pipeline network. The research exploits results from previous work and it is suitable for systems handling different client priorities and in which device reliability has an important short-term impact on operations.

Keywords

Algebraic modeling Flow networks Oil pipeline networks (max, +) theory Schedule optimization System reliability 

Notes

Acknowledgments

This research has been supported by Thales Group France, and by the PCP (Post-graduate Cooperation Program) between Venezuela and France involving the collaboration between the academic institutions: ULA (in Spanish: Universidad de Los Andes)—research laboratory: CEMISID in Mérida, Venezuela and the INSA (in French: Université de Lyon, INSA Lyon, Ampère (UMR5005)) in Lyon, France; and the industrial partners Thales Group France and PDVSA (in Spanish: Petróleos de Venezuela Sociedad Anónima), the Venezuelan oil company. Industrial data for model validation has been granted by PDVSA.

References

  1. 1.
    K. Quintero, E. Niel, J. Aguilar et al. (Max, +) Optimization model for scheduling operations in a flow network with preventive maintenance tasks, in Proceedings of The World Congress on Engineering and Computer Science 2013, WCECS 2013. Lecture Notes in Engineering and Computer Science, vol. 2 (San Francisco, USA, 2013), pp. 1036–1041, 23–25 Oct 2013Google Scholar
  2. 2.
    K. Quintero, E. Niel, J. Aguilar et al., Scheduling operations in a flow network with flexible preventive maintenance: a (max, +) approach. Eng. Lett. 22, 24–33 (2014)Google Scholar
  3. 3.
    M. Alsaba, J.-L. Boimond, S. Lahaye, On the control of flexible manufacturing production systems by dioid algebra (originally in french: Sur la commande des systèmes flexibles de production manufacturière par l’algèbre des dioïdes). Revue e-STA, Sciences et Technologies de l’Automatique 4, 3247–3259 (2007)Google Scholar
  4. 4.
    A. Nait-Sidi-Moh, M.-A. Manier, A. El Moudni et al. Petri net with conflicts and (max, +) algebra for transportation systems, in 11th IFAC Symposium on control in transportation systems, 11 pp. 548–553Google Scholar
  5. 5.
    W. Ait-Cheik-Bihi, A. Nait-Sidi-Moh, M. Wack, Conflict management and resolution using (max, +) algebra: application to services interaction, in Evaluation and Optimization of Innovative Production Systems of Goods and Services: 8th International Conference of Modeling and Simulation—MOSIM’10 (2010)Google Scholar
  6. 6.
    S.G. Ponnambalam, N. Jawahar, B.S. Girish, An ant colony optimization algorithm for flexible job shop scheduling problem, in New Advanced Technologies (2010), http://www.intechopen.com/books/new-advanced-technologies/An Ant Colony Optimization Algorithm for Flexible Job Shop Scheduling Problem. Accessed 11 Feb 2014
  7. 7.
    W. Moore, A. Starr, An intelligent maintenance system for continuous cost-based prioritization of maintenance activities. Computers in industry (2006), doi: 10.1016/j.compind.2006.02.008
  8. 8.
    K. Yang, X. Liu, A bi-criteria optimization model and algorithm for scheduling in a real-world flow shop with setup times, in Proceedings of the International Conference on Intelligent Computation Technology and Automation (ICICTA), vol.1, (2008), pp. 535–539Google Scholar
  9. 9.
    Z. Zhao, G. Zhang, Z. Bing, Job-shop scheduling optimization design based on an improved GA, in Proceedings of the 10th World Congress on Intelligent Control and Automation (WCICA), 2012, pp. 654–659 Google Scholar
  10. 10.
    C. Zeng, J. Tang, H. Zhu, Two heuristic algorithms of job scheduling problem with inter-cell production mode in hybrid operations of machining, in 25th Chinese Control and Decision Conference (CCDC), 2013, pp. 1281–1285Google Scholar
  11. 11.
    J. Rojas-D’Onofrio, J. González, E. Boutleux et al. Path search algorithm minimizing interferences with envisaged operations in a pipe network, in Proceedings of the European Control Conference, ECC’09 (2009)Google Scholar
  12. 12.
    K. Quintero, E. Niel, J. Rojas-D’Onofrio, Optimizing process supervision in a flow network in terms of operative capacity and failure risk, in 15th International congress on automation, systems and instrumentation, 2011Google Scholar
  13. 13.
    F. Baccelli, G. Cohen, G. Jan-Olsder, J.-P. Quadrat, Synchronization and Linearity an Algebra for Discrete Event Systems. (Wiley, New York, 2001)Google Scholar
  14. 14.
    G. Cohen, S. Gaubert, J.-P. Quadrat, Sandwich algebra (originally in french: lalg`ebre des sandwichs). Pour la science 328, 56–63 (2005)Google Scholar
  15. 15.
    L. Houssin, S. Lahaye, J.-L. Boimond, Just-in-time control under constraints of (max, +)-linear systems (originally in french: Commande en juste-à-temps sous contraintes de systèmes (max, +)-linéaires). Journal Européen des systèmes automatisés—JESA 39, 335–350 (2005)CrossRefGoogle Scholar
  16. 16.
    G. Nasri I, Habchi, R. Boukezzoula, An algebraic max-plus model for HVLV systems scheduling and optimization with repetitive and flexible periodic preventive maintenance: just-in-time production, in 9th International Conference of Modeling, Optimization and SimulationMOSIM’12, 2012Google Scholar
  17. 17.
    Z. Königsberg, Modeling, analysis and timetable design of a helicopter maintenance process based on timed event petri nets and max-plus algebra. Neural Parallel Sci Comput. 18, 1–12 (2010)MATHMathSciNetGoogle Scholar
  18. 18.
    S. Gaubert, Performance evaluation of (max, +) automata. IEEE Trans. Autom. Control 40, 2014–2025 (1995)CrossRefMATHMathSciNetGoogle Scholar
  19. 19.
    S. Lahaye, J. Komenda, J.-L. Boimond, Modular modeling with (max, +) automata (originally in french: Modélisation modulaire à l’aide d’automates (max, +)), in Conférence internationale francophone d’automatique—CIFA. (Grenoble, France 2012)Google Scholar
  20. 20.
    J. Komenda, S. Lahaye, J.-L. Boimond, The synchronous product of (max, +) automata (originally in french: Le produit synchrone des automates (max, +)). Special issue of Journal Européen des Systèmes Automatisés—JESA 43, 1033–1047 (2009)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • Karla Quintero
    • 1
  • Eric Niel
    • 2
  • José Aguilar
    • 3
  • Laurent Piétrac
    • 2
  1. 1.Thales GroupVélizyFrance
  2. 2.INSALyonFrance
  3. 3.ULAMéridaVenezuela

Personalised recommendations