Modelling supply networks with partial differential equations

D’Apice, C.; Manzo, R.; Piccoli, B.

doi:10.1090/S0033-569X-09-01129-1

Authors: C. D’Apice, R. Manzo and B. Piccoli
Journal: Quart. Appl. Math. 67 (2009), 419-440
MSC (2000): Primary 35L65, 90B30
DOI: https://doi.org/10.1090/S0033-569X-09-01129-1
Published electronically: May 5, 2009
MathSciNet review: 2547634
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Abstract: A continuum-discrete model for supply networks is introduced. The model consists of a system of conservation laws: a conservation law for the goods density and an evolution equation for the processing rate. The network is formed by subchains and nodes at which, motivated by real cases, two routing algorithms are considered: the first maximizes fluxes taking into account the goods’ final destinations, while the second maximizes fluxes without constraints. We analyze waves produced at nodes and equilibria for both algorithms, relating the latter to production rates in real supply networks. In particular, we show how the model can reproduce the well-known Bullwhip effect.

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