# 157-0474/02 – Quantitative Methods (KMk)

 Gurantor department Department of Systems Engineering Credits 5 Subject guarantor doc. Mgr. Ing. František Zapletal, Ph.D. Subject version guarantor doc. Mgr. Ing. František Zapletal, Ph.D. Study level undergraduate or graduate Requirement Compulsory Year 3 Semester summer Study language Czech Year of introduction 2019/2020 Year of cancellation Intended for the faculties EKF Intended for study types Bachelor
Instruction secured by
VRA31 Ing. Blanka Bazsová, Ph.D.
CHY0034 Mgr. Ing. Lucie Chytilová, Ph.D.
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
Part-time Credit and Examination 6+6

### 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.

### Teaching methods

Lectures
Individual consultations
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 + input-output analysis Final exam

LMS Moodle

### Other requirements

Credit - linear programming + network analysis + quick test during semester Final exam

### Prerequisities

Subject has no prerequisities.

### 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. 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. 5. Transport problems - specification of traffic problems, classification of traffic problems, searching for acceptable solution (VAM, MSR, IM), search for optimal solution - MODI. 6. Multicriterial linear programming - motivation and application, solution dominance, aggregation of purpose functions according to defined weights, tasks with compromise solution. 7. 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. 8. 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. 9. 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. 10. Input-output analysis - visualization of the system (elements and flows), basic logic and assumptions. 11. Input-output analysis - chess board tables, equilibria in Leontief's models (sales and inputs), applications.

### Conditions for subject completion

Part-time form (validity from: 2019/2020 Winter semester)
Min. number of pointsMax. počet pokusů
Credit and Examination Credit and Examination 100 (100) 51
Credit Credit 45 (45) 23 2
Test LP - lineární programování Written test 20  10 2
Test SA - síťová analýza Written test 15  8 2
Test STA - strukturní analýza Written test 10  5 2
Examination Examination 55  28 3
Mandatory attendence participation: Condition for passing: - active participation, - successful completion of individual tests at given dates, - exam - combined (test + oral exam)

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Conditions for subject completion and attendance at the exercises within ISP: Condition for passing: - active participation, - successful completion of individual tests at given dates, - exam - combined (test + oral exam)

Show history

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2022/2023 (B0413A050012) Economics and Management (S02) Business Administration K Czech Ostrava 2 Compulsory study plan
2022/2023 (B0413A050012) Economics and Management (S03) Management K Czech Ostrava 2 Compulsory study plan
2021/2022 (B0312A050001) Public Economics and Administration K Czech Valašské Meziříčí 2 Compulsory study plan
2021/2022 (B0312A050001) Public Economics and Administration K Czech Ostrava 2 Compulsory study plan
2021/2022 (B0312A050001) Public Economics and Administration K Czech Šumperk 2 Compulsory study plan
2021/2022 (B0413A050012) Economics and Management (S02) Business Administration K Czech Ostrava 2 Compulsory study plan
2021/2022 (B0413A050012) Economics and Management (S03) Management K Czech Ostrava 2 Compulsory study plan
2021/2022 (B0311A050004) Applied Economics (S01) International Economic Relations K Czech Ostrava 2 Compulsory study plan
2021/2022 (B0311A050004) Applied Economics (S02) Economic Development K Czech Ostrava 3 Compulsory study plan
2020/2021 (B0312A050001) Public Economics and Administration K Czech Ostrava 2 Compulsory study plan
2020/2021 (B0312A050001) Public Economics and Administration K Czech Šumperk 2 Compulsory study plan
2020/2021 (B0312A050001) Public Economics and Administration K Czech Valašské Meziříčí 2 Compulsory study plan
2020/2021 (B0413A050012) Economics and Management (S02) Business Administration K Czech Ostrava 2 Compulsory study plan
2020/2021 (B0413A050012) Economics and Management (S03) Management K Czech Ostrava 2 Compulsory study plan
2020/2021 (B0311A050004) Applied Economics (S01) International Economic Relations K Czech Ostrava 2 Compulsory study plan
2020/2021 (B0311A050004) Applied Economics (S02) Economic Development K Czech Ostrava 3 Compulsory study plan
2019/2020 (B0312A050001) Public Economics and Administration K Czech Ostrava 2 Compulsory study plan
2019/2020 (B0413A050012) Economics and Management (S03) Management K Czech Ostrava 2 Compulsory study plan
2019/2020 (B0312A050001) Public Economics and Administration K Czech Šumperk 2 Compulsory study plan
2019/2020 (B0312A050001) Public Economics and Administration K Czech Valašské Meziříčí 2 Compulsory study plan
2019/2020 (B0311A050004) Applied Economics (S01) International Economic Relations K Czech Ostrava 2 Compulsory study plan
2019/2020 (B0413A050012) Economics and Management (S02) Business Administration K Czech Ostrava 2 Compulsory study plan
2019/2020 (B0311A050004) Applied Economics (S02) Economic Development K Czech Ostrava 3 Compulsory study plan

### Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner