In this paper, we extend the model for supply chains developed in . The model consists of partial differential equations governing the dynamics on each processor. Furthermore, a modelling of different types of vertices is motivated and discussed. Then, optimization problems are introduced and numerically investigated. A comparison of computing times shows the efficiency of partial differential equations for solving supply chain problems.
"Modelling and optimization of supply chains on complex networks." Commun. Math. Sci. 4 (2) 315 - 330, June 2006.