A continuum-discrete model for supply chains dynamics

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].

[1]  Axel Klar,et al.  Gas flow in pipeline networks , 2006, Networks Heterog. Media.

[2]  Mauro Garavello,et al.  Source-Destination Flow on a Road Network , 2005 .

[3]  CIRO D’APICE,et al.  Packet Flow on Telecommunication Networks , 2006, SIAM J. Math. Anal..

[4]  Mathematisches Forschungsinstitut Oberwolfach,et al.  Hyperbolic Conservation Laws , 2004 .

[5]  P. I. Richards.  Shock Waves on the Highway , 1956 .

[6]  H. Holden,et al.  A mathematical model of traffic flow on a network of unidirectional roads , 1995 .

[7]  M J Lighthill,et al.  On kinematic waves II. A theory of traffic flow on long crowded roads , 1955, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[8]  Ciro D'Apice,et al.  A fluid dynamic model for supply chains , 2006, Networks Heterog. Media.

[9]  M. Herty,et al.  Network models for supply chains , 2005 .

[10]  A. Bressan.  Hyperbolic Systems of Conservation Laws , 1999 .

[11]  J. Lebacque.  THE GODUNOV SCHEME AND WHAT IT MEANS FOR FIRST ORDER TRAFFIC FLOW MODELS , 1996 .

[12]  C. Dafermos.  Hyberbolic Conservation Laws in Continuum Physics , 2000 .

[13]  P. Lax.  Hyperbolic systems of conservation laws , 2006 .

[14]  Dirk Helbing,et al.  SUPPLY AND PRODUCTION NETWORKS: FROM THE BULLWHIP EFFECT TO BUSINESS CYCLES , 2004 .

[15]  B. Piccoli,et al.  Traffic Flow on a Road Network Using the Aw–Rascle Model , 2006 .

[16]  Axel Klar,et al.  Modeling, Simulation, and Optimization of Traffic Flow Networks , 2003, SIAM J. Sci. Comput..

[17]  Axel Klar,et al.  Existence of Solutions for Supply Chain Models Based on Partial Differential Equations , 2007, SIAM J. Math. Anal..

[18]  Mauro Garavello,et al.  Traffic Flow on a Road Network , 2005, SIAM J. Math. Anal..

[19]  Axel Klar,et al.  Modelling and optimization of supply chains on complex networks , 2006 .

[20]  Benedetto Piccoli,et al.  Traffic circles and timing of traffic lights for cars flow , 2005 .

[21]  C. M. Dafermos,et al.  Hyberbolic [i.e. Hyperbolic] conservation laws in continuum physics , 2005 .

[22]  Carlos F. Daganzo,et al.  A theory of supply chains , 2003 .

[23]  D. Helbing,et al.  Physics, stability, and dynamics of supply networks. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[24]  Christian A. Ringhofer,et al.  Kinetic and Fluid Model Hierarchies for Supply Chains , 2003, Multiscale Model. Simul..

[25]  D. Armbruster,et al.  Kinetic and fluid models for supply chains supporting policy attributes , 2007 .