Abstract
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.
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Acknowledgments
This project was started when D.A. was a part time professor at the Department of Mechanical Engineering, Eindhoven University of Technology. Helpful discussions with Erjen Lefeber and Ivo Adan on transient queueing models are gratefully acknowledged. Discussions with Hubert Missbauer and Reha Uzsoy helped to clarify the experiments on transient queuing and the relationship between clearing function models and the production planning problem. This research was supported by a grant from the Volkswagen Foundation under the program on Complex Networks.
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Armbruster, D., Fonteijn, J. & Wienke, M. Modeling production planning and transient clearing functions. Logist. Res. 5, 133–139 (2012). https://doi.org/10.1007/s12159-012-0087-8
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DOI: https://doi.org/10.1007/s12159-012-0087-8