Industrial Mathematics: Modeling, Simulation, and Optimization

En presentation över ämnet: "Industrial Mathematics: Modeling, Simulation, and Optimization"— Presentationens avskrift:

1 Industrial Mathematics: Modeling, Simulation, and Optimization
Short Overview of Current Activities and Competences in the Mathematics Department Prof. M.G. Larson

2 Industrial Mathematics
Mathematics and statistics play a more and more important role in industry due to the rapid development of computer resources (data storage and computation) Problem Model Simulation Results Optimization

3 Interdisciplinary Challenge!
Math Applications Computer Science Industrial mathematics generally involves: Many types of mathematics Computer science Engineering, economics, and so on New challenges for education, collaboration, and research!

4 Competences in Industrial Math at UmU
Differential equations including modeling and computer based methods Stochastic modeling and risk analysis Discrete modeling and optimization Mathematical statistics and data analysis Strong theoretical basis is now starting to be transferred into industrial applications. Process IT to play an important role in this process

5 Reference Activity: Fraunhofer ITWM
Fraunhofer Chalmers Center for Industrial Mathematics. Started in Göteborg in 2000 Now employs approx 35 fulltime people 15 Msek/year new project money from industry Mother institute in Kaiserslautern 10.5 MEuro budget in 2006 (20% female scientists 31% female PhD candidates)

6 Stem Profile Estimation and Optimization of Bucking A pilot study
A project within the frame of Process IT Komatsu Forest, Umeå and Department of Mathematics Umeå university

7 Forester in Action

8 Maximizing the Value of a Tree
The forester uses an optimization algorithm to determine where the bucking of the tree should be done in order to optimize the value. The optimization algorithm is based on a prediction (mathematical model) of the stem form. The prediction of the stem form uses measurements of the stem recorded by the forester. Small improvements has large economic impact since volumes are large! In the future prices are expected to change rapidly (reflecting demand) which leads to new demands on optimization.

9 Goals of the Project Evaluation of different models for estimation of stem profiles. Which model should be used? Investigation of the optimization bucking algorithm. What is the potential gain?

10 Stem Profile Estimation
Volume Diameter(Height) Stem profile comparison between the estimation algorithms and data from harvesting. Error in estimated volume. Typical volume of a tree is 1m3.

11 Stem Profile Estimation
All of the algorithms in the literature uses the total height of the stem as in data, which is hard to estimate for a standing tree and thus give unsecure estimations. All models demands adjustment of the internal parameters which needs some time to be calculated. Conclusion: Model used by Komatsu is better than academic models. Some possible improvements identified.

12 Bucking Optimization Conclusion: There are improvements to be made with a new bucking algorithm. An efficient optimization algorithm (real time) is hard to develop: a frontline research problem.

13 Optimering av produktionsplanering vid Trelleborg Sealing Solutions
Examensarbete Joel Persson Peter Sundsten

14 Trelleborg Sealing Solutions
Ligger ca en mil norr om Skellefteå Ca 275 Anställda Omsätter 245 MSEK Tillverkar tätningar i gummi. T.ex. O-ringar många olika produkter! Önskar ett hjälpmedel för att planera produktionen optimalt Leveransschema finns men det sker uppdateringar av detta som måste pareras

15 Två viktiga kostnader Ställkostnad, kostnad för att starta upp en ny process Lagerkostnad, man betalar en andel av det totala värdet av de produkter som ligger i lagret

16 Två olika planeringar Orderlista Två olika planeringar
Artikel Dag 1 Dag 2 Dag 3 Dag4 50 25 Två olika planeringar Artikel Dag 1 Dag 2 Dag 3 Dag4 50 25 Två ställkostnader, ingen lagerkostnad. Artikel Dag 1 Dag 2 Dag 3 Dag4 75 25 En ställkostnad, lagerkostnad för 25 st o-ringar i två dagar.

17 Dynamisk programmering
50 25 50 75 25 75 Nätverket beskriver möjliga vägar Dynamisk programmering finner den bästa vägen

18 Resultat DP-programmet Artikel Antal omstarter Lagerkostnad
Ställkostnad Total kostnad 22 7110 kr 7979 kr 15089 kr TSS Artikel Antal omstarter Lagerkostnad Ställkostnad Total kostnad 27 43642 kr 9793 kr 53434 kr

19 Slutsatser Genom att använda optimering kan den totala produktionskostnaden sänkas Programvaran förbättras nu och skall testas i större omfattning i ett aktuellt exjobb Optimering kan användas för att automatisera och styra industriella processer samtidigt som besluten blir bättre och mer konsistenta Har du en process som du vill optimera?