Different phenomena appearing in managing supply chains can be described by continuous models. In this talk, we focus on the mathematical modeling as well as on techniques for simulation and optimization of those supply chain models.
We propose a network model which is suitable for the approximation of continuous material flows and survey the underlying fundamentals. The model is based on partial and ordinary differential equations and can be related to a mixed-integer programming model (MIP) for optimization purposes. To reduce the computational effort of large-scale instances, we show that under certain
conditions on the objective functional the MIP is in fact equivalent to a linear programming problem only. Since the original model is purely deterministic, random breakdown of processors, delivery failure or uncertain demand are neglected.