The basic partial differential equation (PDE) models for supply chain networks with re-entrant nodes and their macroscopic are proposed. However, through numerical examples, the basic continuum models do not perform well for multiple re-entrant systems. Then, a new state equation considering the re-entrant degree of the products is introduced to improve the effectiveness of the basic continuum models. The applicability of the modified continuum models for re-entrant supply chains is illustrated through numerical examples. Finally, based on the modified continuum model, numerical examples of different re-entrant degrees are given, meanwhile, the changes in the WIP and outflux are analyzed in details for multiple re-entrant supply chain systems.
Fenglan He. Ming Dong. Xiaofeng Shao. "Modeling and Analysis of Material Flows in Re-Entrant Supply Chain Networks Using Modified Partial Differential Equations." J. Appl. Math. 2011 (SI1) 1 - 14, 2011. https://doi.org/10.1155/2011/325690