Existence of solutions to Cauchy problems for a mixed continuum-discrete model for supply chains and networks
We consider a continuum-discrete model for supply chains based on partial differential equations. The state space is formed by a graph: The load dynamics obeys to a continuous evolution on each arc, while at nodes the good density is conserved, while the processing rate is adjusted. To uniquely dete...
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Published in | Journal of mathematical analysis and applications Vol. 362; no. 2; pp. 374 - 386 |
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Main Authors | , , |
Format | Journal Article |
Language | English |
Published |
Amsterdam
Elsevier Inc
15.02.2010
Elsevier |
Subjects | |
Online Access | Get full text |
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Summary: | We consider a continuum-discrete model for supply chains based on partial differential equations. The state space is formed by a graph: The load dynamics obeys to a continuous evolution on each arc, while at nodes the good density is conserved, while the processing rate is adjusted. To uniquely determine the dynamics at nodes, the through flux is maximized, with the minimal possible processing rate change. Existence of solutions to Cauchy problems is proven. The latter is achieved deriving estimates on the total variation of the density flux, density and processing rate along a wave-front tracking approximate solution. Then the extension to supply networks is showed. |
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ISSN: | 0022-247X 1096-0813 |
DOI: | 10.1016/j.jmaa.2009.07.058 |