Modeling production planning and transient clearing functions

The production planning problem, that is, to determine the production rate of a factory in the future, requires an aggregate model for the production flow through a factory. The canonical model is the clearing function model based on the assumption that the local production rate instantaneously adjusts to the one given by the equilibrium relationship between production rate (flux) and work in progress (wip), for example, characterized by queueing theory. We will extend current theory and modeling for transient clearing functions by introducing a continuum description of the flow of product through the factory based on a partial differential equation model for the time evolution of the wip-density and the production velocity. It is shown that such a model improves the mismatch between models for transient production flows and discrete event simulations significantly compared to other clearing function approaches.