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Networks and Heterogeneous Media

2006, Volume 1, Issue 3: 379-398. doi: 10.3934/nhm.2006.1.379
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A fluid dynamic model for supply chains

  • 1.
    Department of Information Engineering and Applied Mathematics, University of Salerno, via Ponte Don Melillo, 84084 Fisciano (SA)
  • 2.
    Dipartimento di Ingegneria dell'Informazione e Matematica Applicata, University of Salerno, Via Ponte Don Melillo, 84084 - Fiscano (SA)
  • Received: 01 November 2005 Revised: 01 March 2006

  • Primary: 35L65, 90B30; Secondary: 34B45.

  • The paper deals with a fluid dynamic model for supply chains. A mixed continuum-discrete model is proposed and possible choices of solutions at nodes guaranteeing the conservation of fluxes are discussed. Fixing a rule a Riemann solver is defined and existence of solutions to Cauchy problems is proved.

    Citation: Ciro D'Apice, Rosanna Manzo. A fluid dynamic model for supply chains[J]. Networks and Heterogeneous Media, 2006, 1(3): 379-398. doi: 10.3934/nhm.2006.1.379

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  • The paper deals with a fluid dynamic model for supply chains. A mixed continuum-discrete model is proposed and possible choices of solutions at nodes guaranteeing the conservation of fluxes are discussed. Fixing a rule a Riemann solver is defined and existence of solutions to Cauchy problems is proved.


  • This article has been cited by:

    1. Alfredo Cutolo, Benedetto Piccoli, Luigi Rarità, An Upwind-Euler Scheme for an ODE-PDE Model of Supply Chains, 2011, 33, 1064-8275, 1669, 10.1137/090767479
    2. L. Forestier--Coste, S. Göttlich, M. Herty, Data-Fitted Second-Order Macroscopic Production Models, 2015, 75, 0036-1399, 999, 10.1137/140989832
    3. Mauro Garavello, Benedetto Piccoli, 2013, Chapter 6, 978-1-4614-6242-2, 143, 10.1007/978-1-4614-6243-9_6
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    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
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    9. Ciro D'Apice, Peter I. Kogut, Rosanna Manzo, On relaxation of state constrained optimal control problem for a PDE-ODE model of supply chains, 2014, 9, 1556-181X, 501, 10.3934/nhm.2014.9.501
    10. 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
    11. Mauro Garavello, Benedetto Piccoli, Conservation laws on complex networks, 2009, 26, 0294-1449, 1925, 10.1016/j.anihpc.2009.04.001
    12. Ming Dong, Fenglan He, A new continuous model for multiple re-entrant manufacturing systems, 2012, 223, 03772217, 659, 10.1016/j.ejor.2012.07.002
    13. Simone Göttlich, Axel Klar, 2013, Chapter 8, 978-3-642-32159-7, 395, 10.1007/978-3-642-32160-3_8
    14. 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
    15. Ciro D'Apice, Peter I. Kogut, Rosanna Manzo, On Approximation of Entropy Solutions for One System of Nonlinear Hyperbolic Conservation Laws with Impulse Source Terms, 2010, 2010, 1687-5249, 1, 10.1155/2010/982369
    16. Simone Göttlich, Michael Herty, Ute Ziegler, Modeling and optimizing traffic light settings in road networks, 2015, 55, 03050548, 36, 10.1016/j.cor.2014.10.001
    17. Benedetto Piccoli, Andrea Tosin, 2012, Chapter 112, 978-1-4614-1805-4, 1748, 10.1007/978-1-4614-1806-1_112
    18. 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
    19. Simone Göttlich, Michael Herty, Melanie Luckert, 2017, Chapter 2, 978-3-319-63955-0, 21, 10.1007/978-3-319-63957-4_2
    20. Maria Pia D'Arienzo, Luigi Rarità, 2020, 2293, 0094-243X, 420041, 10.1063/5.0026464
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    22. Ke Han, Terry L. Friesz, Tao Yao, A Variational Approach for Continuous Supply Chain Networks, 2014, 52, 0363-0129, 663, 10.1137/120868943
    23. Ciro D’Apice, Maria Pia D’Arienzo, Peter I. Kogut, Rosanna Manzo, On boundary optimal control problem for an arterial system: Existence of feasible solutions, 2018, 18, 1424-3199, 1745, 10.1007/s00028-018-0460-4
    24. RINALDO M. COLOMBO, PAOLA GOATIN, BENEDETTO PICCOLI, ROAD NETWORKS WITH PHASE TRANSITIONS, 2010, 07, 0219-8916, 85, 10.1142/S0219891610002025
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    27. Benedetto Piccoli, Andrea Tosin, 2009, Chapter 576, 978-0-387-75888-6, 9727, 10.1007/978-0-387-30440-3_576
    28. S. Göttlich, M. Herty, C. Ringhofer, U. Ziegler, Production systems with limited repair capacity, 2012, 61, 0233-1934, 915, 10.1080/02331934.2011.615395
    29. CIRO D'APICE, BENEDETTO PICCOLI, VERTEX FLOW MODELS FOR VEHICULAR TRAFFIC ON NETWORKS, 2008, 18, 0218-2025, 1299, 10.1142/S0218202508003042
    30. Zlatinka Dimitrova, Flows of Substances in Networks and Network Channels: Selected Results and Applications, 2022, 24, 1099-4300, 1485, 10.3390/e24101485
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  • © 2006 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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