A level set approach to modeling general service rules in supply chains

The need for service rules, or policies, in supply chains arises if not all the parts processed in the chain are considered identical, but are distinguished by certain attributes. We develop and analyze a methodology to model arbitrary service rules in large supply chains based on a kinetic (traffic flow like) theory and a level set approach. The final result is a system of hyperbolic conservation laws for the densities of parts, grouped by their attributes. The validity of the model is verified against discrete event simulations for several test cases.