OPF:INMNPEMM Economic and Mathematical Meth - Course Information

INMNPEMM Economic and Mathematical Methods

Extent and Intensity

2/1/0. 5 credit(s). Type of Completion: zk (examination).

Teacher(s)

doc. RNDr. David Bartl, Ph.D. (lecturer)
doc. RNDr. David Bartl, Ph.D. (seminar tutor)

Guaranteed by

doc. RNDr. David Bartl, Ph.D.
Department of Informatics and Mathematics – School of Business Administration in Karvina
Contact Person: Mgr. Radmila Krkošková, Ph.D.

Timetable

Wed 13:05–14:40 A216

• Timetable of Seminar Groups:

INMNPEMM/01: Wed 14:45–15:30 A216, D. Bartl

Prerequisites (in Czech)

FAKULTA(OPF) && TYP_STUDIA(N) && FORMA(P)

Course Enrolment Limitations

The course is only offered to the students of the study fields the course is directly associated with.

The capacity limit for the course is 30 student(s).
Current registration and enrolment status: enrolled: 15/30, only registered: 3/30

fields of study / plans the course is directly associated with

• Managerial Informatics (programme OPF, N_MI)

Course objectives

To provide a deeper insight into exact quantitative methods for modelling economic situations. To develop an understanding of the theoretical foundations of selected methods and models, particularly optimization methods in mathematical programming and their application in economic disciplines, and to acquire practical skills in using software tools for solving problems on a computer, especially Microsoft Excel.

Learning outcomes

The student is able to model selected phenomena and problems arising in technical or economic practice as linear programming problems, transform multi-criteria and goal programming problems into mathematical programming problems with a single objective function, solve mathematical programming problems (particularly linear programming problems) using appropriate software tools, apply the theory of linear and non-linear programming to verify the optimality of a given solution (the KKT conditions), determine an optimal portfolio using the Markowitz model, the Sharpe model, and related portfolio optimization models, manage and analyse projects using the Critical Path Method (CPM) and the Programme Evaluation and Review Technique (PERT).

Syllabus

• 1. Economic and mathematical modelling
  Mathematics and economics, classification of models, mathematical tools as a language for modelling economic phenomena. Functions of one and several real variables, matrices, inverse matrices, vectors, systems of linear equations with n unknowns, mathematical functions in MS Excel.
• 2. Optimization problems and function extrema
  Optimization problems, mathematical programming, equivalent formulations of optimization problems, local and global extrema, existence of optimal solutions. Convex and concave functions, convex sets, saddle points, Karush-Kuhn-Tucker conditions, duality in mathematical programming.
• 3. Linear programming
  Linear programming, optimal resource allocation, basic solutions, degenerate and non-degenerate solutions, the one-phase and two-phase simplex method. Primal and dual linear programming problems, duality, the transportation problem, the assignment problem, examples of practical applications.
• 4. Multi-criteria and goal programming
  Multi-criteria programming, goal programming, non-dominated solutions, Pareto-optimal solutions, scalarization methods.
• 5. Mathematical methods of portfolio optimization
  Portfolio optimization, return, risk, the efficient frontier, efficient portfolios, stochastic portfolio models. The Sharpe model, the Markowitz model, the single-index model, the beta coefficient. Applications of MS Excel Solver for portfolio optimization problems.
• 6. Optimization problems on graphs and networks
  Graphs and networks, minimum spanning tree, shortest path problem, maximum flow problem. Network diagrams, the Critical Path Method (CPM), the Program Evaluation and Review Technique (PERT), the Graphical Evaluation and Review Technique (GERT). Applications of these methods to practical problems.

Literature

required literature
• RAMÍK, Jaroslav; David BARTL and Radomír PERZINA. Ekonomicko-matematické metody: Distanční studijní text. Karviná: Slezská univerzita v Opavě, Obchodně podnikatelská fakulta v Karviné, 2026. info

recommended literature
• WISNIEWSKI, Mik; Farhad SHAFTI and Wee Meng YEO. Quantitative Analysis for Decision Makers. 8th Edition. Pearson, 2025. ISBN 978-1-292-46985-0. info
• OSBORNE, Martin J. Mathematical methods for economic theory. 2023. URL info
• ŠUBRT, Tomáš. Ekonomicko-matematické metody. 3. upr. a rozš. vyd. Plzeň: Vydavatelství a nakladatelství Aleš Čeněk, 2019. ISBN 978-80-7380-762-7. info
• MANSINI, Renata; Włodzimierz OGRYCZAK and M. Grazia SPERANZA. Linear and Mixed Integer Programming for Portfolio Optimization. Springer, 2015. ISBN 978-3-319-18481-4. Available from: https://doi.org/10.1007/978-3-319-18482-1. info
• KLEIN, M. Mathematical Methods for Economics, 2nd Edition. Pearson New International Edition, 2013. ISBN 978-1292039183. info
• RAMÍK, J., PERZINA, R. Moderní metody hodnocení a rozhodování . Karviná : SU v Opavě, OPF v Karviné, 2008. ISBN 978-80-7248-497-3. info
• J. Jablonský. Operační výzkum - kvantitativní modely pro ekonomické rozhodování 3. vyd. Profesional Publishing, Praha, 2007. ISBN 978-80-86946-44-3. info
• RAMÍK, J., ČEMERKOVÁ, Š., MIELCOVÁ, E. Operační analýza pro ekonomy. Karviná, OPF SU, 2004. ISBN 80-7248-199-3. info
• GUÉRET, Christelle; Christian PRINS and Marc SEVAUX. Applications of optimization with Xpress-MP. Blisworth (UK): Dash Optimization, 2002. ISBN 0-9543503-0-8. info

Teaching methods

lectures and seminars (exercises, problems, examples and case studies), independent preparation of a seminar paper (a portfolio optimization project)

Assessment methods

Requirements for the student: regular study, attendance at seminars min. 70 %, seminar paper, final test.
Assessment: attendance at seminars, seminar paper (30 % of assessment), written test (70 % of assessment).
Assessment methods: independent preparation of a seminar paper (a portfolio optimization project), final written test (several problems from the areas taught).

Language of instruction

Czech

Further comments (probably available only in Czech)

The course can also be completed outside the examination period.
General note: Individuální studijní zátěž - zkoušející doc. Bartl.

• Enrolment Statistics (recent)
  
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