## Sticky separation in the wast paper treatment

The industrial treatment of waste paper in order to obtain recovered paper involves several steps of preparation. One important step is the separation of stickies that are normally attached to the paper. If not properly separated, remaining stickies reduce the quality of the recovered paper or even disrupt the production process. For the separation itself a chain of separators is used. Each one has an input feed and two output streams called the accept and the reject. In the accept the fibers are concentrated, whereas the reject has a higher concentration of stickies. However, after just a single step, the accept still has too many stickies, and the reject too many fibers. To get a proper separation, several separators have to be assembled into a network.

From a mathematical point of view this problem can be seen as a multi-commodity network flow problem with a nonlinear distribution function at each node. We formulate a nonlinear mixed-integer programming model for the simultaneous selection of a subset of separators, the network's topology, and the optimal setup of each separator. Numerical results are obtained via a linearization of the nonlinearities and the use of linear mixed-integer solvers.

• ETH Zürich

### Releted talks

Sticky-Abscheidung bei der Altpapieraufbereitung, GOR Workshop Technical Operations Research (TOR), Annweiler am Trifels, Germany, 10.3.2015.

1. Optimization of Sticky Separation in Waste Paper Processing , MINLP 2014 Workshop, Pittsburgh (PA), USA, 3.6.2014.

2. Optimization of Sticky Separation in Waste Paper Processing, Applied Mathematics and Optimization Seminar, Helmut Schmidt University, Hamburg, Germany, 6.5.2014.

3. Solving Nonlinear Engineering Problem with Piecewise-Linear Approximation Techniques, 20th International Symposium on Mathematical Programming ISMP 2009, Chicago (IL), USA, 27.8.2009.

4. Mixed-Integer Linear Programming and Paper Recycling (Poster Session), German-American Frontiers of Engineering Symposium 2009, Potsdam, Germany, 23.4.2009.

5. Optimization of Sticky Separation in Waste Paper Processing, AIMS 2008, Conference of the American Institute for Mathematical Science, Arlington (TX), USA, 19.5.2008.

6. Mixed-Integer Linear Programming and Paper Recycling, Technische Universität Darmstadt, Germany, 16.4.2008.

### Releted publications

Armin Fügenschuh, Christine Hayn, Dennis Michaels, Mixed-Integer Linear Methods for Layout-Optimization of Screening Systems in Recovered Paper Production , Optimization and Engineering, Vol. 15, No. 2, pp. 533 - 573, 2014. (Also available as ZIB Technical Report ZR-12-44 , 2012.)

1. Mirjam Dür, Armin Fügenschuh, Alexander Martin, Samuel Schabel, Christine Schönberger, Klaus Villforth, Method for Setting and/or Optimizing a Sorting System Separating Acceptable Material from Unacceptable Material , and Sorting System, European Patent Application, EP 22 55 034, 2010.

2. Mirjam Dür, Armin Fügenschuh, Alexander Martin, Samuel Schabel, Christine Schönberger, Klaus Villforth, Verfahren zum Einstellen und/oder Optimieren einer einen Gutstoff von einem Schlechtstoff trennenden Sortieranlage und Sortieranlage , German Patent, DE 10 2008 013 034, 2008.

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