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

Michael Schönlein, Thomas Makuschewitz, Fabian Wirth and Bernd Scholz-Reiter

European Journal of Operational Research, 2013, vol. 229, issue 1, 179-189

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.

Keywords: Robustness and sensitivity analysis; Stochastic processes; Queueing; Uncertainty modeling; Supply chain management (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:229:y:2013:i:1:p:179-189

DOI: 10.1016/j.ejor.2013.02.002

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