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Measurement and optimization of robust stability of multiclass queueing networks: Applications in dynamic supply chains

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  • Schönlein, Michael
  • Makuschewitz, Thomas
  • Wirth, Fabian
  • Scholz-Reiter, Bernd
Abstract
Multiclass queueing networks are an essential tool for modeling and analyzing complex supply chains. Roughly speaking, stability of these networks implies that the total number of customers/jobs in the network remains bounded over time. In this context robustness characterizes the ability of a multiclass queueing network to remain stable, if the expected values of the interarrival and service times distributions are subject to uncertain shifts. A powerful starting point for the stability analysis of multiclass queueing networks is the associated fluid network. Based on the fluid network analysis we present a measure to quantify the robustness, which is indicated by a single number. This number will be called the stability radius. It represents the magnitude of the smallest shift of the expected value of the interarrival and/or service times distributions so that the associated fluid network looses the property of stability. The stability radius is a worst case measure and is a conceptual adaptation from the dynamical systems literature. Moreover, we provide a characterization of the shifts that destabilize the network. Based on these results, we formulate a mathematical program that minimizes the required network capacity, while ensuring a desired level of robustness towards shifts of the expected values of the interarrival times distributions. This approach provides a new view on long-term robust production capacity allocation in supply chains. The capabilities of our method are demonstrated using a real world supply chain.

Suggested Citation

  • Schönlein, Michael & Makuschewitz, Thomas & Wirth, Fabian & Scholz-Reiter, Bernd, 2013. "Measurement and optimization of robust stability of multiclass queueing networks: Applications in dynamic supply chains," European Journal of Operational Research, Elsevier, vol. 229(1), pages 179-189.
    • Handle: RePEc:eee:ejores:v:229:y:2013:i:1:p:179-189
    DOI: 10.1016/j.ejor.2013.02.002
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    References listed on IDEAS

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    1. Dimitris Bertsimas & David Gamarnik & Alexander Anatoliy Rikun, 2011. "Performance Analysis of Queueing Networks via Robust Optimization," Operations Research, INFORMS, vol. 59(2), pages 455-466, April.
    2. J. G. Dai & J. H. Vande Vate, 2000. "The Stability of Two-Station Multitype Fluid Networks," Operations Research, INFORMS, vol. 48(5), pages 721-744, October.
    3. Roy, Bernard, 2010. "Robustness in operational research and decision aiding: A multi-faceted issue," European Journal of Operational Research, Elsevier, vol. 200(3), pages 629-638, February.
    4. John M. Mulvey & Robert J. Vanderbei & Stavros A. Zenios, 1995. "Robust Optimization of Large-Scale Systems," Operations Research, INFORMS, vol. 43(2), pages 264-281, April.
    5. Dawei Bai & Tamra Carpenter & John Mulvey, 1997. "Making a Case for Robust Optimization Models," Management Science, INFORMS, vol. 43(7), pages 895-907, July.
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    Cited by:

    1. Aijun Liu & John Fowler & Michele Pfund, 2016. "Dynamic co-ordinated scheduling in the supply chain considering flexible routes," International Journal of Production Research, Taylor & Francis Journals, vol. 54(1), pages 322-335, January.
    2. Xiaoli Zhang & Qing Wang & Binglong Zhao & Jiafu Su, 2024. "Exploring the Vulnerability of Supply Chain Networks from the Perspective of Network Collaborative Relationships," Journal of the Knowledge Economy, Springer;Portland International Center for Management of Engineering and Technology (PICMET), vol. 15(3), pages 11041-11062, September.
    3. Sagawa, Juliana Keiko & Nagano, Marcelo Seido & Speranza Neto, Mauro, 2017. "A closed-loop model of a multi-station and multi-product manufacturing system using bond graphs and hybrid controllers," European Journal of Operational Research, Elsevier, vol. 258(2), pages 677-691.

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