# Demand robust arrangement of operating units and equipment by combining optimization and simulation

In this project we combine methods of mathematical optimization and material flow simulation in order to determine assignments of operation units and machines. These assignments should consider the transport system and should be robust with respect to the requirements. Uncertainties with respect to the development of the production program and changes of the transports between the units and machines will be taken into account.

Aspects like the adaptability of the factory or the possibility of extending the factory or changing some of the machines will be considered.

## Motivation and technical background

Globalization and the growing dynamics of the markets pose new challenges for companies. Due to shorter product life cycles and increasing requirements of the customers regarding the quality and other objectives the production programs are changed more often with the affect that changes of the factories and the production areas are necessary. Here factory planning and methods of the “Digital Factory“ are applied.

Currently layout problems in factory planning are often solved with heuristics without any performance guarantees. Furthermore exact methods of mathematical optimization can find exact solutions only rather small instances, although lots of quite restrictive assumptions are made.

One task in factory planning is the determination of the position of the operation units and machines as well as the positioning of the paths and the planning of the transport system. Although the layout highly influences the operations scheduling and the other way round, both perspectives are usually considered individually. We want to test via simulation whether the determined layouts lead to problems with the transport system or the workflow. If this is the case, new aspects should be included in the optimization models.

The decisions in factory planning highly influence future processes in the factory. But there are high uncertainties with respect to the future developments, e.g. the amount of transport between the operation unit or machines. Then one task in factory planning is to decide if and how the layout has to be adjusted.

## Goals

In this project we consider the problem to determine the optimal arrangements of operation units and machines. Given data of the factory and of the machines and operation units we look for provably good solutions with respect to the weighted transportation amount. For solving these problems we use methods of mathematical optimization using appropriate relaxations of the associated integer programming models. The quality of the solutions is verified using simulations. If these show that some aspect is not included in the mathematical models sufficiently well, then the models are extended.

By the close connection of mathematical optimization and simulation we want to iteratively enlarge the realizability and flexibility of the found solution. Here the IMAB resorts to examples of real-world problems and simulations where the analysis is also done in the virtual reality laboratory considering 3D-models of the factories. A main goal of this project is to determine when the extended mathematical models for the optimal arrangement of the operation units and machines should be used and in which cases the use of simulation has advantages.

Uncertainties of the transport intensity will be considered in the mathematical models. We will study which robustness concepts are suited for the use in practice. From time to time an adjustment of the layout might be advantageous. But the costs of such adjustments can hardly be predicted. Here simulations allow the test of several scenarios. The results can then be used in the mathematical models.

## Involved Scientists

### Prof. Dr.-Ing. Uwe Bracht

Research Group Anlagenprojektierung und Materialflusslogistik

Institute of Plant Engineering and Fatigue Analysis

Clausthal University of Technology

Room 226, Leibnizstraße 32, 38678 Clausthal-Zellerfeld

E-Mail: uwe.bracht@imab.tu-clausthal.de

Phone: +49 5323 72-2588

Fax: +49 5323 72-3516

### Jun.-Prof. Dr. Anja Fischer

Research group Optimization

Institute for Numerical and Applied Mathematics

University of Göttingen

Room 118, Lotzestraße 16-18, 37083 Göttingen

E-Mail: a.fischer@math.uni-goettingen.de

Phone: +49 551 39-20035

Fax: +49 551 39-33944

### Dipl.-Wirtschaftsing. Thomas Krüger

Arbeitsgruppe Anlagenprojektierung und Materialflusslogistik

Institut für Maschinelle Anlagentechnik und Betriebsfestigkeit

Technische Universität Clausthal

Raum 221, Leibnizstraße 32, 38678 Clausthal-Zellerfeld

E-Mail: thomas.krueger@imab.tu-clausthal.de

Telefon: +49 5323 72-2826

Fax: +49 5323 72-3516

## Some preliminary work in this area (2010-2016)

- Anjos, M., Fischer, A., Hungerländer, P. (2016) Solution approaches for the double-row equidistant facility layout. Operations Research Proceedings 2014: Selected Papers of the Annual International Conference of the German Operations Research Society (GOR), RWTH Aachen University, Germany, September 2-5, 2014 (Herausgeber: Lübbecke, M., Letmathe, P., Peis, B., Walther, G.). S. 17-23.
- Anjos, M., Fischer, A., Hungerländer, P. (2015). Solution approaches for equidistant double-and multi-row facility layout problems. Les Cahiers du GERAD G-2015-06.
- Arnhold, D. (2013). Digitale Produktionsprozessplanung variantenreicher Produkte unter Berücksichtigung von intervallbasierten Eingangsdaten (Bd. 29 - Herausgeber: Uwe Bracht). Aachen: Shaker Verlag.
- Bracht, U., Krüger, T. (Dezember 2015). Von der Virtualität zur Realität - Fabrikplanung. TUContact.
- Bracht, U., Geckler, D., Wenzel, S. (2011). Digitale Fabrik. Berlin: Springer-Verlag.
- Brosch, P. (2014). Smarte digitale Layoutplanung (Bd. 32- Herausgeber: Uwe Bracht). Aachen: Shaker Verlag.
- Fischer, A., Fischer, F., Hungerländer, P. (2015). New exact approaches to row layout problems. Preprint-Serie des Instituts für Numerische und Angewandte Mathematik 2015-11.
- Fischer, A., Fischer, F., Hungerländer, P. (2015). A new exact approach to the space-free double row layout problem. Angenommen für Operations Research Proceedings 2015.
- Götze, U., Müller, E., Schütz, A., Helmberg, C., Meynerts, L., Rösch, N., Nizielski, S., Lau, A. (2010). Planung energieeffizienter Fabriksysteme. Tagungsband zum 1. Internationalen Kolloquium des Spitzentechnologieclusters eniPROD, S.519-549.
- Sontag, T.-M. (2014). Smarte Fabrikplanung (Bd. 31 - Herausgeber: Uwe Bracht). Aachen: Shaker Verlag.