Production Networks with Stochastic Machinery Default
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We present a model of production networks that includes random breakdowns of individual processors. The defaults of processors are exponentially distributed and the time-continuous formulation of network dynamics yields a coupled PDE-ODE system with Markovian switching. Its solution is a piecewise deterministic process, which allows us to use a modified stochastic simulation algorithm to trace stochastic events and to simulate the deterministic behavior of the network between them. The impact of stochastic default is illustrated with an exemplary Monte-Carlo simulation.
KeywordsSupply Chain Switching Point Production Network Product Density Markovian Switching
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- 1.Davis, M.H.A.: Markov Models and Optimisation. Monograph on Statistics and Applied Probability 49, Chapmand & Hall, London (1993)Google Scholar
- 2.D’Apice, C., Göttlich, S., Herty, M., Piccoli, B.: Modeling, Simulation, and Optimization of Supply Chains: A Continuous Approach. SIAM (2010)Google Scholar
- 5.Göttlich, S, Herty, M., Klar, A.: Network models for supply chains. Comm. Math. Sci. 3(4), 545–559 (2005)Google Scholar
- 6.Göttlich, S., Martin, S., Sickenberger, T.: Time-continuous production networks with random breakdowns. Networks and Heterogeneous Media (NHM) 6(4), 695–714 (2011) DOI: 10.3934/nhm.2011.6.695Google Scholar
- 7.Kelly, F.P., Zachary, S., Ziedins, I. (eds.): Stochastic Networks: Theory and Applications. Oxford University Press, Oxford (2002)Google Scholar