2010
DOI: 10.1016/j.jmaa.2009.07.058
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Existence of solutions to Cauchy problems for a mixed continuum-discrete model for supply chains and networks

Abstract: We consider a continuum-discrete model for supply chains based on partial differential\ud equations. The state space is formed by a graph: The load dynamics obeys to a continuous\ud evolution on each arc, while at nodes the good density is conserved, while the processing\ud rate is adjusted. To uniquely determine the dynamics at nodes, the through flux is\ud maximized, with the minimal possible processing rate change. Existence of solutions to\ud Cauchy problems is proven. The latter is achieved deriving estim… Show more

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Cited by 22 publications
(12 citation statements)
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“…In contrast, macroscopic models describe the average behavior of the production system in terms of part density or flow. They naturally arise from microscopic limits and are usually based on ordinary differential equations (ODEs) [15], hyperbolic partial differential equations (PDEs) [1,5,6,8,11] or a mixture of both [4,7,14]. We refer to [3] and the references therein for a comprehensive overview of macroscopic production models.…”
mentioning
confidence: 99%
“…In contrast, macroscopic models describe the average behavior of the production system in terms of part density or flow. They naturally arise from microscopic limits and are usually based on ordinary differential equations (ODEs) [15], hyperbolic partial differential equations (PDEs) [1,5,6,8,11] or a mixture of both [4,7,14]. We refer to [3] and the references therein for a comprehensive overview of macroscopic production models.…”
mentioning
confidence: 99%
“…The well-posedness of the Riemann problem 7, 22- 24, as well as that of the corresponding Cauchy problem, is proved in [56], [87]. An extension of the model (22) has been proposed in [57], [60] to treat the case of supply chains with spatially and temporally depending capacities. Therein, j D j .t; x/ and equation 22is replaced by u j D .…”
Section: Product Flow In Supply Chainsmentioning
confidence: 99%
“…Among the many examples where such systems arise are traffic flow [24,25,29,31], production networks [21,23,30], telecommunication networks [22], gas flow in pipe networks [3, 11-13, 15, 16] or water flow in canals [4,5,28,35]. Mathematically, flow problems on networks are boundary value problems where the boundary value is implicitly defined by a coupling condition.…”
Section: Introductionmentioning
confidence: 99%