Industrial Mathematics: Modeling, Simulation, and Optimization

Industrial Mathematics: Modeling, Simulation, and Optimization

Short Overview of Current Activities and Competences in the Mathematics

Department

Prof. M.G. Larson

2023-04-22

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

Optimization2023-04-22

Interdisciplinary Challenge!

Math

ApplicationsComputer Science

2008-01-203

Industrial mathematics generally involves: • Many types of mathematics• Computer science • Engineering, economics, and so

on

New challenges for education, collaboration, and research!

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

2023-04-22

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)

2008-01-205

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

2008-01-206

Forester in Action

2008-01-207

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.

2008-01-208

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?

2008-01-209

Stem Profile Estimation

• Stem profile comparison between the estimation algorithms and data from harvesting.

• Error in estimated volume. Typical volume of a tree is 1m3.

2008-01-2010

Diameter(Height) Volume

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.

2008-01-2011

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.

2008-01-2012

Optimering av produktionsplaneringvid Trelleborg Sealing Solutions

Joel Persson Peter SundstenExamensarbete

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

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

Två olika planeringar

Artikel Dag 1 Dag 2 Dag 3 Dag4469906017 0 50 0 25

Artikel Dag 1 Dag 2 Dag 3 Dag4469906017 0 75 25 25

Två ställkostnader, ingen lagerkostnad.

Artikel Dag 1 Dag 2 Dag 3 Dag4

469906017 0 50 0 25

Orderlista

Två olika planeringar

En ställkostnad, lagerkostnad för 25 st o-ringar i två dagar.

Dynamisk programmering

• Nätverket beskriver möjliga vägar• Dynamisk programmering finner den bästa vägen

2550

75

0

0 D0 0 D350 D20 D1 25 D4

0

75

50

0

25

Resultat

DP-programmet

Artikel Antal omstarter Lagerkostnad Ställkostnad Total kostnad

469906017 22 7110 kr 7979 kr 15089 kr

TSS

Artikel Antal omstarter Lagerkostnad Ställkostnad Total kostnad

469906017 27 43642 kr 9793 kr 53434 kr

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?