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Quantitative Methods

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Course Unit Code157-0374/01
Number of ECTS Credits Allocated5 ECTS credits
Type of Course Unit *Compulsory
Level of Course Unit *First Cycle
Year of Study *Second Year
Semester when the Course Unit is deliveredWinter Semester
Mode of DeliveryFace-to-face
Language of InstructionCzech
Prerequisites and Co-Requisites Course succeeds to compulsory courses of previous semester
Name of Lecturer(s)Personal IDName
NEM191Ing. Radek Němec, Ph.D.
ZAP149doc. Mgr. Ing. František Zapletal, Ph.D.
CHY0034Mgr. Ing. Lucie Chytilová, Ph.D.
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.
Learning Outcomes of the Course Unit
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.
Course Contents
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.
Recommended or Required Reading
Required Reading:
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.
FÁBRY, Jan. Matematické modelování. Praha: Professional Publishing, 2011. ISBN 9788074310669.
JABLONSKÝ, Josef. Operační výzkum: Kvantitativní modely pro ekonomické rozhodování. 3. vyd. Praha: Professional Publishing, 2007. 323 s. ISBN 978-80-86946-44-3.
PRICE, A. Joshua. Quantitative Methods. Independently published, 2023. 293 p. ISBN 979-8387351877.
Recommended Reading:
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.
DOSKOČIL, Radek. Kvantitativní metody. Brno, Akademické nakladatelství CERM, 2019. 262 s. ISBN: 978-80-214-5716-4.
FIALA, Petr. Operační výzkum: nové trendy. Praha: Professional Publishing, 2010. ISBN 9788074310362.
HILLIER, Frederick S. a Gerald J. LIEBERMAN. Introduction to operations research. 9th ed. New York: McGraw-Hill Higher Education, c2010. ISBN 9780073376295.
Planned learning activities and teaching methods
Lectures, Tutorials, Other activities
Assesment methods and criteria
Task TitleTask TypeMaximum Number of Points
(Act. for Subtasks)
Minimum Number of Points for Task Passing
Credit and ExaminationCredit and Examination100 (100)51
        CreditCredit45 (45)23
                Test LP - lineární programováníWritten test20 10
                Test SA - síťová analýzaWritten test15 8
                Test STA - strukturní analýzaWritten test10 5
        ExaminationExamination55 28