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Networks and Heterogeneous Media

2007, Volume 2, Issue 4: 661-694. doi: 10.3934/nhm.2007.2.661
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A continuum-discrete model for supply chains dynamics

  • 1.
    Istituto per le Applicazioni del Calcolo "M. Picone", IAC-CNR Viale del Policlinico, 137, 00161, Rome
  • 2.
    Dipartimento di Ingegneria dell’Informazione e Matematica Applicata, Università degli Studi di Salerno, Via Ponte don Melillo, 1, Fisciano (SA) 84084
  • 3.
    Dipartimento di Ingegneria dell'Informazione e Matematica Applicata, University of Salerno, Via Ponte Don Melillo, 84084 - Fiscano (SA)
  • 4.
    Istituto per le Applicazioni del Calcolo "M. Picone", IAC-CNR, Viale del Policlinico 137, 00161 Roma
  • Received: 01 April 2007 Revised: 01 August 2007

  • 90B10, 65M06, 65N05.

  • This paper is focused on continuum-discrete models for supply chains. In particular, we consider the model introduced in [10], where a system of conservation laws describe the evolution of the supply chain status on sub-chains, while at some nodes solutions are determined by Riemann solvers. Fixing the rule of flux maximization, two new Riemann Solvers are defined. We study the equilibria of the resulting dynamics, moreover some numerical experiments on sample supply chains are reported. We provide also a comparison, both of equilibria and experiments, with the model of [15].

    Citation: Gabriella Bretti, Ciro D’Apice, Rosanna Manzo, Benedetto Piccoli. A continuum-discrete model for supply chains dynamics[J]. Networks and Heterogeneous Media, 2007, 2(4): 661-694. doi: 10.3934/nhm.2007.2.661

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  • This paper is focused on continuum-discrete models for supply chains. In particular, we consider the model introduced in [10], where a system of conservation laws describe the evolution of the supply chain status on sub-chains, while at some nodes solutions are determined by Riemann solvers. Fixing the rule of flux maximization, two new Riemann Solvers are defined. We study the equilibria of the resulting dynamics, moreover some numerical experiments on sample supply chains are reported. We provide also a comparison, both of equilibria and experiments, with the model of [15].


  • This article has been cited by:

    1. C. D'Apice, R. Manzo, B. Piccoli, Existence of solutions to Cauchy problems for a mixed continuum-discrete model for supply chains and networks, 2010, 362, 0022247X, 374, 10.1016/j.jmaa.2009.07.058
    2. Simone Göttlich, Patrick Schindler, Optimal inflow control of production systems with finite buffers, 2015, 20, 1553-524X, 107, 10.3934/dcdsb.2015.20.107
    3. P. I. Kogut, R. Manzo, On Vector-Valued Approximation of State Constrained Optimal Control Problems for Nonlinear Hyperbolic Conservation Laws, 2013, 19, 1079-2724, 381, 10.1007/s10883-013-9184-5
    4. Simone Göttlich, Axel Klar, Patrick Schindler, Discontinuous Conservation Laws for Production Networks with Finite Buffers, 2013, 73, 0036-1399, 1117, 10.1137/120882573
    5. C. D’Apice, R. Manzo, B. Piccoli, Modelling supply networks with partial differential equations, 2009, 67, 0033-569X, 419, 10.1090/S0033-569X-09-01129-1
    6. C. D'Apice, R. Manzo, B. Piccoli, Numerical Schemes for the Optimal Input Flow of a Supply Chain, 2013, 51, 0036-1429, 2634, 10.1137/120889721
    7. Simone Göttlich, Michael Herty, Christian Ringhofer, 2012, Chapter 11, 978-0-85729-643-6, 265, 10.1007/978-0-85729-644-3_11
    8. Zlatinka Dimitrova, Flows of Substances in Networks and Network Channels: Selected Results and Applications, 2022, 24, 1099-4300, 1485, 10.3390/e24101485
    9. Dieter Armbruster, Simone Göttlich, Michael Herty, A Scalar Conservation Law with Discontinuous Flux for Supply Chains with Finite Buffers, 2011, 71, 0036-1399, 1070, 10.1137/100809374
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    12. Agnes Dittel, Simone Göttlich, Ute Ziegler, Optimal design of capacitated production networks, 2011, 12, 1389-4420, 583, 10.1007/s11081-010-9123-1
    13. Maria Pia D'Arienzo, Luigi Rarità, 2020, 2293, 0094-243X, 420041, 10.1063/5.0026464
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    15. Mauro Garavello, Benedetto Piccoli, Time-varying Riemann solvers for conservation laws on networks, 2009, 247, 00220396, 447, 10.1016/j.jde.2008.12.017
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