## INMBAOPA Operational Analysis

Summer 2023
Extent and Intensity
2/1/0. 6 credit(s). Type of Completion: zk (examination).
Teacher(s)
Guaranteed by
Department of Informatics and Mathematics - School of Business Administration in Karvina
Contact Person: Mgr. Radmila Krkošková, Ph.D.
Timetable
Thu 10:35–12:10 A412
• Timetable of Seminar Groups:
INMBAOPA/01: Thu 12:15–13:00 A412, R. Perzina
Prerequisites (in Czech)
FAKULTA ( OPF ) && TYP_STUDIA ( B ) && ( FORMA ( P ) || FORMA ( Z ))
Course Enrolment Limitations
The course is only offered to the students of the study fields the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The aim of this course is to teach the students basic principles of mathematical methods for modeling economical situations. The students should manage theoretical background of selected methods and models and be able to use Microsoft Excel Solver for solving operational analysis problems on PC.
Syllabus
• 1. Principles and methods of Operational Analysis
History and principles of Operational Analysis, stages in application of Operational Analysis, classification of Operational Analysis branches.
2. Linear programming
Economical and mathematical model, economical meaning of particular parts of mathematical model, basic elements of linear programming (LP), graphic representation of a feasible solutions set of a two-variables LP problem and solving the problem. General economical and mathematical model, base solutions of a linear programming model. The principle of Simplex method, the number of LP problem optimal solutions determination, solving the LP problem by Excel Solver.
3. Duality in linear programming
Duality as a relation between two LP problems, construction of dual problem, relations between primal and dual problem, economical interpretation of optimal solutions of both problems, sensitivity analysis.
4. Application of linear programming
Construction of the mathematical model for the following problems: Cutting stock problem, Nutrition problem, Financial project analysis, Portfolio optimization problem, Production problem, Transportation Problem. Solving the problems by Excel. Interpretation of results.
5. Optimization problems on graphs
Basic elements, basic definitions. Planar graph, complete graph, loop, cycle. Minimal spanning tree algorithm, Eulerian path, the shortest path and maximal flow algorithms.
6. Project Management
Project graph, project analysis by critical path method – CPM. Project analysis by method PERT, basic characteristics of project analysis, i.e. mean value of activity time, standard deviation of activity time, mean value of project completion time and standard deviation of project completion time, probability of finishing the project in planned time.
Literature
required literature
• HILLIER, F.S., LIEBERMAN, G.J., NAG, B., BASU, P., 2017. Introduction to Operations Research. New York: Mc Graw Hill. ISBN 978-9339221850
• RARDIN, R.L., 2016. Optimization in Operations Research. Cambridge: Pearson. ISBN 978-0134384559
recommended literature
• TAHA, H.A., 2016. Operations Research: An Introduction. Cambridge: Pearson. ISBN 978-0134444017
• CARTER, M., Price, C.C., RABADI, G., 2018. Operations Research: A Practical Introduction. Boca Raton: CRC Press. ISBN 978-1498780100
• KOCAY, W., KREHER, D.L., 2016. Graphs, Algorithms, and Optimization. Boca Raton: CRC Press. ISBN 978-1482251166
Teaching methods
lectures, seminar classes, class discussion
Assessment methods
Compulsory participation in seminars at least 50%, seminar paper (30% evaluation) final examination test (70% evaluation). The minimum required number of points for passing the course is 60% of the total number of points.
Language of instruction
English