Course code InfT4039

Credit points 2

Mathematical Modelling

Total Hours in Course80

Number of hours for lectures8

Number of hours for seminars and practical classes24

Independent study hours48

Date of course confirmation04.09.2019

Responsible UnitDepartment of Control Systems

Course developer

author Vadības sistēmu katedra

Jeļena Koroļova

Mg. paed.

Course abstract

Students study Mathematical Modelling as part of the Operations Research, simulate and test systems for decision-making, acquire practical skills in Mathematical Programming (Linear Programming, Integer Programming and Integer Nonlinear Programming), modelling with MS Excel optimization tool Solver, Project Management software MS Office Project and a comparison of alternatives by The Analytic Hierarchy Process.

Learning outcomes and their assessment

After completing the course student will have:
Knowledge about Operations Research methods for decision planning and making management with computer (tests, home works and practical works);
Skills - build the mathematical models with MS Excel and MS Project for operations research and decision making with AHP (tests, home works and practical works);
Competence – knowledge and ability for optimal and environmental safety decision planning and making process with Information Technologies (tests, home works and practical works).

Course plan

1 Introduction. Mathematical Programming. Classification of methods.
2 Linear programming (LP) and MS Excel Solver. Use of limited resources for profit (income) maximization.
3. Linear programming (LP) and MS Excel Solver. Use of limited resources for profit (income) maximization.
4 Linear programming (LP) and MS Excel Solver. Use of limited resources for cost (time) minimization.
5 Linear programming (LP) and MS Excel Solver. Use of limited resources for cost (time) minimization.
6 Integer linear programming and MS Excel Solver. Optimization of the use of production resources.
7 Integer linear programming and MS Excel Solver. Optimization of the use of production resources.
8 Integer nonlinear programming (INLP) with MS Excel Solver. Optimization of the use of production resources.
9 1st test (LP, IP, INLP).
10 Network models for managing processes or projects. Critical Path Method (CPM).
11 Project execution time risk assessment with Program Evaluation and Review Techniques (PERT).
12 Introduction to the MS Office Project app for project or process planning.
13 Linear programming in project networks for cost optimization.
14 2nd test (CPM, LP networks).
15 The Analytical Hierarchy Process (AHP) for solving applied energy problems.
16 The defence of individual and independent work - the application of the AHP method.

Requirements for awarding credit points

Successfully passed the formal test with a grade at least 40% of the course total score.

Description of the organization and tasks of students’ independent work

Tasks for the independent work are included in e-studies (http://estudijas.llu.lv).
There is one independent and individual work in the semester.

Criteria for Evaluating Learning Outcomes

1. The formal test cumulative assessment depends on two tests (70 %) and independent individual work (30 %) ratings.
2. Students who are mostly studying independently, or wish to improve the cumulative assessment take the written formal test (70 %). Independent individual work assessment (30 %) will also be taken into account.

Compulsory reading

1. Koroļova J. Lekciju konspekti, laboratorijas darbu uzdevumi un papildmateriāli. http://estudijas.llu.lv
2. Rau N. S. Optimization Principles: Practical Applications to the Operation and Markets of the Electric Power Industry. Piscataway, N.J.: IEEE Press; Wiley-Interscience, 2003. 339 p.
3. Taha H. A. Operations Research: An Introduction. 9th ed. Upper Saddle River, N.J.: Pearson Education/Prentice Hall, 2011. 824 p.

4. Moore J.H., Weatherford L.R. Decision modelling with Microsoft Excel. Prentice Hall, 2001. 1020 p.

Further reading

1. Frolova L. Matemātiskā modelēšana ekonomikā un menedžmentā. Rīga: Izglītības soļi, 2005. 438 lpp.
2. Peļņa M., Gulbe M. Optimizācijas uzdevumi ekonomikā. Rīga: Datorzinību centrs, 2003. 160 lpp.
3. Praude V., Beļcikovs J. Loģistika. Rīga: Vaidelote, 2003. 541 lpp.

Periodicals and other sources

1. E-žurnāls "Operation Research" [tiešsaiste]. Research Society of America. ISSN 0030-364X. [Skatīts 21.11.2016.] Pieejams: http://or.journal.informs.org/

Notes

General study course for Professional Bachelor’s study programme “Applied Energy Engineering”