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

Full-text PDF Free Access

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