Communications in Mathematical Sciences

Volume 8 (2010)

Number 4

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

Pages: 909 – 930

DOI: http://dx.doi.org/10.4310/CMS.2010.v8.n4.a7

Author

Christian Ringhofer

Abstract

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.

Keywords

Supply chains; traffic flow models; level sets; Boltzmann equation; fluid limits

2010 Mathematics Subject Classification

65N35

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