Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Modelling supply networks with partial differential equations

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 | References | Similar Articles | Additional Information

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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Additional Information

C. D'Apice
Affiliation: Department of Information Engineering and Applied Mathematics, University of Salerno, Fisciano (SA), Italy
Email: dapice@diima.unisa.it

R. Manzo
Affiliation: Department of Information Engineering and Applied Mathematics, University of Salerno, Fisciano (SA), Italy
Email: manzo@diima.unisa.it

B. Piccoli
Affiliation: Istituto per le Applicazioni del Calcolo “Mauro Picone”, Consiglio Nazionale delle Ricerche, Roma, Italy
Email: b.piccoli@iac.cnr.it

DOI: https://doi.org/10.1090/S0033-569X-09-01129-1
Keywords: Conservation laws, supply networks
Received by editor(s): October 3, 2007
Published electronically: May 5, 2009
Article copyright: © Copyright 2009 Brown University

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