157-0374/02 – Quantitative Methods (KM)
| Gurantor department | Department of Systems Engineering | Credits | 6 |
| 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 | 2 | Semester | winter |
| | Study language | Czech |
| Year of introduction | 2024/2025 | Year of cancellation | |
| Intended for the faculties | EKF | Intended for study types | Bachelor |
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:
Recommended literature:
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
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction
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