# 157-0574/01 – Quantitative methods (KMe)

 Gurantor department Department of Systems Engineering Credits 5 Subject guarantor prof. Ing. Jana Hančlová, CSc. Subject version guarantor doc. Mgr. Ing. František Zapletal, Ph.D. Study level undergraduate or graduate Requirement Compulsory Year 2 Semester summer Study language English Year of introduction 2019/2020 Year of cancellation Intended for the faculties EKF Intended for study types Bachelor
Instruction secured by
HAN60 prof. Ing. Jana Hančlová, CSc.
ZAP149 doc. Mgr. Ing. František Zapletal, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+2

### Subject aims expressed by acquired skills and competences

The aim of the course is methodological knowledge as systemic application of discipline, especially in the areas of linear programming and network analysis. The application of selected quantitative methods reinforces students' logical and systemic skills in solving decision-making problems in economic systems.

Lectures
Tutorials

### Summary

1. Operation research as a systemic basis for quantitative decision making. Development and systemic features of operation research. Process of economic-mathematical modeling. Classification of operation research methods, usability in solving economic problems. 2. Introduction to linear programming (LP) + general solution of optimization problem + parts of mathematical model + set of possible solutions + possible number of solution of LP + different types of LP. 3. Graphical solution of LP problem - general procedure, limitations for using graphical solution, possible sets of acceptable solutions, consequences of limitation of the equation in models, sensitivity analysis of optimum in graphical solution, possible solutions of LP problems. 4. Canonical form of LP problem, simplex table, algorithm of solution for single-phase and two-phase simplex method, individual steps of simplex method, interpretation of simplex tables. 5. Duality of LP problem - the importance of duality, basic theorems on duality, symmetric and asymmetric dual models, shadow prices and their use for sensitivity analysis, solution stability intervals. 6. Transport problems - specification of traffic problems, classification of traffic problems, searching for acceptable solution (VAM, MSR, IM), search for optimal solution - MODI. 7. Multicriterial linear programming - motivation and application, solution dominance, aggregation of purpose functions according to defined weights, tasks with compromise solution. 8. Introduction to network analysis (SA) and graph theory - embedding in the framework of project management, target and possibility of application, classification and definition of network analysis methods, project specification and network graph creation, fictional edges. 9. CPM - time analysis in network graph, types of reserves and their importance, critical path and its analysis, percentage of criticality and possibilities of use from the perspective of risk management, project criticism, linear diagram, analysis of project resources. 10. PERT method - stochastic time analysis, density of activity duration distribution and mean and variability characteristics, density distribution of the earliest possible end date of the whole project and corresponding characteristics, typical problem of using PERT method.

### Compulsory literature:

HILLIER, Frederick S. a Gerald J. LIEBERMAN. Introduction to operations research. 5th ed. New York: McGraw-Hill, c1990. ISBN 0-07-909758-8. WISNIEWSKI, Mik. Quantitative methods for decision makers. 5th ed. Harlow: Financial Times Prentice Hall, 2009. ISBN 978-0-273-71207-7. TAHA, Hamdy A. Operations research: an introduction. 9th ed., international ed. Upper Saddle River: Pearson, c2011. ISBN 978-0-13-139199-4.

### Recommended literature:

RUSZCZYŃSKI, Andrzej P. Nonlinear optimization. Princeton: Princeton University Press, c2006. ISBN 0-691-11915-5. RAMÓN, J. and S. C. MATEO. Management Science, Operations Research and Project Management Modelling, Evaluation, Schceduling, Monitoring. London: Taylor and Francis, 2016. RAVINDRAN, A. Operations research and management science handbook. Boca Raton: CRC Press, 2008.

### Way of continuous check of knowledge in the course of semester

Credit - linear programming + network analysis + quick test during semester Exam - combined (test + oral exam)

LMS Moodle

### Other requirements

Credit - linear programming + network analysis + quick test during semester Exam - combined (test + oral exam)

### Prerequisities

Subject codeAbbreviationTitleRequirement
151-0500 Math A Mathematics A Compulsory

### Co-requisities

Subject has no co-requisities.

### Subject syllabus:

1. Operation research as a systemic basis for quantitative decision making. Development and systemic features of operation research. Process of economic-mathematical modeling. Classification of operation research methods, usability in solving economic problems. 2. Introduction to linear programming (LP) + general solution of optimization problem + parts of mathematical model + set of possible solutions + possible number of solution of LP + different types of LP. 3. Graphical solution of LP problem - general procedure, limitations for using graphical solution, possible sets of acceptable solutions, consequences of limitation of the equation in models, sensitivity analysis of optimum in graphical solution, possible solutions of LP problems. 4. Canonical form of LP problem, simplex table, algorithm of solution for single-phase and two-phase simplex method, individual steps of simplex method, interpretation of simplex tables. 5. Duality of LP problem - the importance of duality, basic theorems on duality, symmetric and asymmetric dual models, shadow prices and their use for sensitivity analysis, solution stability intervals. 6. Transport problems - specification of traffic problems, classification of traffic problems, searching for acceptable solution (VAM, MSR, IM), search for optimal solution - MODI. 7. Multicriterial linear programming - motivation and application, solution dominance, aggregation of purpose functions according to defined weights, tasks with compromise solution. 8. Introduction to network analysis (SA) and graph theory - embedding in the framework of project management, target and possibility of application, classification and definition of network analysis methods, project specification and network graph creation, fictional edges. 9. CPM - time analysis in network graph, types of reserves and their importance, critical path and its analysis, percentage of criticality and possibilities of use from the perspective of risk management, project criticism, linear diagram, analysis of project resources. 10. PERT method - stochastic time analysis, density of activity duration distribution and mean and variability characteristics, density distribution of the earliest possible end date of the whole project and corresponding characteristics, typical problem of using PERT method.

### Conditions for subject completion

Full-time form (validity from: 2019/2020 Winter semester)
Min. number of points
Credit and Examination Credit and Examination 100 (100) 51
Credit Credit 45 (45) 23
zápočtový test LP Written test 25  13
Zápočtový test SA Written test 15  8
Rychlotesty na cvičeních Other task type 5  0
Examination Examination 55  28
Mandatory attendence parzicipation: Condition for passing: - 60% participation in exercises - successful completion of individual tests at given dates - at least 23 points Acquired credits are enrolled. Compulsory mass credit tests (enrollment via Edison, 1st regular and 2nd corrective term) - LP - Linear Programming - (min 13 - max 25 points) - SA - Network Analysis - (min 8 - max 15 points) - quick tests during exercise - (max 5 points) Exam - combined (test + oral exam) - min 28, max 55 points.

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2020/2021 (B0311A050005) Applied Economics (S02) International Economic Relations P English Ostrava 2 Compulsory study plan
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2019/2020 (B0311A050005) Applied Economics (S02) International Economic Relations P English Ostrava 2 Compulsory study plan
2019/2020 (B0311A050005) Applied Economics (S01) Economic Development P English Ostrava 3 Compulsory study plan
2019/2020 (B0412A050006) Finance P English Ostrava 2 Compulsory study plan

### Occurrence in special blocks

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