Numerical Methods For Continuum Supply Chain Networks

In recent years, the research on supply chains has become an important topic. There are a lot of mathematical methods used to depict supply chains. The most important two tools are discrete and continuous models. Though the discrete models are more accurate, their drawback is that to maintain them is quite expensive because of their exponentially increasing computing time for large scale systems. A continuum modeling approach can remedy the computational drawback in the case of large quantity and multistage networks. We can find broad applications in future along with the increasing scale of corporations and related supply chains.In this paper, a continuum model with first order hyperbolic partial differential equations of conservation law is employed to model the supply chain networks, and the discontinuous Galerkin finite element method is used to solve the system of equations. It allows us to establish the supercloseness between DG finite element solution and the exact solution by taking the advantage of discontinuity of our approximation space. By means of the projection interpolation and the superclose analysis technique, an O(hr+1)-order optimal convergence error estimate is established under the conditions of connectivity matrix.