In this (more theoretical oriented) research project we describe a company‘s manufacturing assembly lines as network of conveyor belts connecting processing machines. Each machine is assumed to have an individual waiting queue. The system‘s dynamic is described by differential equations. On the conveyor belts the transport PDE is used to model the flow of particles. The waiting queues are described by ODEs. After discretizing all differential equations, a huge mixed-integer linear programming problem is obtained. To solve it, we apply special preprocessing techniques that are usually not included in state-of-the-art mixed-integer linear
solvers.

We apply our techniques to solve a manufacturing system problem for a German toothbrush manufacturer. The practitioners were asking for the maximum manufacturing capacity of their system that does not lead to a collapse from overflowing waiting queues. Our approach was able to successfully address these and other questions.

Partners

• TU Darmstadt

Related talks

• Solving PDEs with MIP Techniques, Veszprem Optimization Conference: Advanced Algorithms VOCAL, Veszprem, Hungary, 13.12.2006.

Related publications

• Armin Fügenschuh, Simone Göttlich, Claus Kirchner, Michael Herty, Alexander Martin, Efficient Reformulation and Solution of a Nonlinear PDE-Controlled Flow Network Model , Computing, Vol. 85, No. 3, pp. 245 – 265, 2009.
• Armin Fügenschuh, Agnes Dittel, Simone Göttlich, Michael Herty, MIP Presolve Techniques for a PDE-based Supply Chain Model , Optimization Methods & Software, Vol. 24, No. 3, pp. 427 – 445, 2009.
• Armin Fügenschuh, Simone Göttlich, Michael Herty, Axel Klar, Alexander Martin, A Discrete Optimization Approach to Large Scale Supply Networks Based on Partial Differential Equations , SIAM Journal on Scientific Computing, Vol. 30, No. pp. 1490 – 1507, 2008.
• Armin Fügenschuh, Simone Göttlich, Michael Herty, An Alternative Modeling Approach for an Integrated Simulation and Optimization of a Class of Production Networks , Hans-O. Günther, Dirk Mattfeld, Lena Suhl (Eds.), Management logistischer Netzwerke, Physica-Verlag, Heidelberg, pp. 45 – 60, 2007.