157-0374/01 – Quantitative Methods (KM)

Gurantor departmentDepartment of Systems EngineeringCredits5
Subject guarantordoc. Mgr. Ing. František Zapletal, Ph.D.Subject version guarantordoc. Mgr. Ing. František Zapletal, Ph.D.
Study levelundergraduate or graduateRequirementCompulsory
Year2Semestersummer
Study languageCzech
Year of introduction2019/2020Year of cancellation
Intended for the facultiesEKFIntended for study typesBachelor
Instruction secured by
LoginNameTuitorTeacher giving lectures
VRA31 Ing. Blanka Bazsová, Ph.D.
BOR0151 Ing. Dominika Bordácsová
CHY0034 Mgr. Ing. Lucie Chytilová, Ph.D.
HAN60 prof. Ing. Jana Hančlová, CSc.
NEM191 Ing. Radek Němec, Ph.D.
SIN0085 Ing. Markéta Šindlerová
STE0405 Ing. Marek Štěpán
SVA0158 Ing. Miloš Švaňa
VOL0133 Ing. Jan Volný
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, structural analysis 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
Tutorials
Other activities

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:

EISELT, H. A. a Carl-Louis Sandblom. Operations Research. 3rd ed. Springer Nature Switzerland AG. 2022. ISBN 9783030971618. KUMAR, Amit a Mangey Ram. Operations Research: Methods, Techniques, and Advancements. Boca Raton: CRC Press, 2022. ISBN 9781003156291. RAJU, N.V.S. Operations Research: Theory and Practice. 1st ed. London: CRC Press. 2019. ISBN 9780367366070.

Recommended literature:

ŠUBRT, Tomáš a kol. Ekonomicko-matematické metody. 3. upravené a rozšířené vydání. Plzeň: Vydavatelství a nakladatelství Aleš Čeněk, 2019. ISBN 978-80-7380-762-7. SHAH, Nita H. a Poonam Prakash MISHRA. Non-Linear Programming: A Basic Introduction. Boca Raton: ImprintCRC Press, 2020. ISBN 9780367613280. SINGLA, Vikas. Operations Research Using Excel. Boca Raton: CRC Press. 2021. ISBN 9781003212966.

Way of continuous check of knowledge in the course of semester

Condition for passing: - credit tests: LP - Linear Programming, SA - Network Analysis, STA - input-output analysis. - final oral exam.

E-learning

Other requirements

Condition for passing: - 60% participation in exercises - successful completion of individual tests at given dates (LP, STA, SA) - at least 23 points: LP - Linear Programming, SA - Network Analysis, STA - Input-output analysis. - at least 28 points for successful 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

Full-time form (validity from: 2020/2021 Winter semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of pointsMax. počet pokusů
Credit and Examination Credit and Examination 100 (100) 51 3
        Credit Credit 45 (45) 23
                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: Podmínka získání zápočtu: - 60 % účast na cvičení, - u každého zápočtového testu LP, STA, SA má student 2 pokusy (1 řádný a 1 opravný) a další 1 pokus v případě, že mu chybí pouze 1 zápočtový test LP nebo STA nebo SA) - pro získání zápočtu musí student dosáhnout alespoň 25 bodů z 45. Podmínka získání zkoušky je získání 28-55 bodů z testů v LMS Moodle a případného ústního dozkoušení ( tj. při získání minimálně 21 bodů v LMS).

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Conditions for subject completion and attendance at the exercises within ISP: Účast na cvičeních nepovinná. Termíny zápočtů lze řešit individuálně s garantem předmětu. Termíny zkoušek dle rozpisu v Edisonu.

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Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner
Subject block without study plan - EKF - P - cs 2021/2022 Full-time Czech Optional EKF - Faculty of Economics stu. block

Assessment of instruction



2023/2024 Winter
2022/2023 Summer
2022/2023 Winter
2021/2022 Summer
2021/2022 Winter
2020/2021 Summer
2020/2021 Winter