| Course Unit Code | 157-0300/01 |
|---|
| Number of ECTS Credits Allocated | 5 ECTS credits |
|---|
| Type of Course Unit * | Compulsory |
|---|
| Level of Course Unit * | First Cycle |
|---|
| Year of Study * | Second Year |
|---|
| Semester when the Course Unit is delivered | Winter Semester |
|---|
| Mode of Delivery | Face-to-face |
|---|
| Language of Instruction | Czech |
|---|
| Prerequisites and Co-Requisites | |
|---|
| Prerequisities | Course Unit Code | Course Unit Title |
|---|
| 151-0300 | Mathematics A |
| Name of Lecturer(s) | Personal ID | Name |
|---|
| HAN60 | prof. Ing. Jana Hančlová, CSc. |
| NEM191 | Ing. Radek Němec, Ph.D. |
| ZAP149 | doc. Mgr. Ing. František Zapletal, Ph.D. |
| CHY0034 | Mgr. Ing. Lucie Chytilová, Ph.D. |
| Summary |
|---|
| The aim of the subject is to make students familiar with basics of the operations research belonging to systems disciplines and solving complex economic problems. Outputs should be knowledge of selected methods of the operations research, its nature, fundamentals, means of use in real situations. Students should be able to formulate problems and consequently design and solve applicable economic-mathematical models using appropriate software tools. |
| Learning Outcomes of the Course Unit |
|---|
• To describe the operations research as an applied systems discipline
• To define basic systems terms and terms from economic and mathematics modeling
• To classify operations research methods
• To explain the substance and application possibilities of the basic methods
• To apply chosen methods model tools to concrete specific problems
• To solve created models with PC use
• To explicate and analyze obtained results
|
| Course Contents |
|---|
1. Operations research – systemic basis for the quantitative approach to decision making. Development and systemic characteristics of the operations research. Economic-mathematical modeling. IT and software support. Methods of the operations research and their classification. Applicability of the subject for real-situation problems solving.
2. Optimization methods, linear programming (LP), principles of mathematical models designing.
3. Basic problems of LP and their characteristics. General model of LP problem.
4. LP problems solving and interpretation. Basic principles for models solving, simplex method.
5. Problem of duality and efficiency of LP problems. Sensitivity analysis of the optimal solution – sensitivity to change of right-hand-side coefficients of constraints, objective function coefficients, adding and removing variables or constraints.
6. Distribution problems. Characteristics of basic problem – balanced and unbalanced problem, basic solution, methods of optimization.
7. Multi-objective programming (dominated/non-dominated solution, aggregation of objective functions using the weights, compromise solution).
8.Introduction to the graph theory,network analysis – possible areas for application, basic terminology and methods. Methodology for network graphs designing.
9. Time analysis in network graphs. Time demands of projects, dates of project activities, critical path, reserves of activities, critical path analysis.
10. Resources analysis. Problem of resource consuption minimizing, project schedule optimization.
11. PERT method (differences from CPM method, probability distribution, involving the risk into network analysis).
|
| Recommended or Required Reading |
|---|
| Required Reading: |
|---|
HILLIER, Frederick S. and Gerald J. LIEBERMAN. Introduction to Operations Research. 9th ed. London: McGraw-Hill, 2009. 1088 pp. ISBN 978-80-077298340.
|
MORAVCOVÁ, Eva a Jitka BAŇAŘOVÁ. Operační výzkum A (kurz v prostředí LMS Moodle, kategorie e-learning). Ostrava: EkF VŠB-TU Ostrava, 2006.
JABLONSKÝ, Josef. Operační výzkum: kvantitativní modely pro ekonomické rozhodování. 3. vyd. Praha: Professional Publishing, 2007. 323 s.
ISBN 978-80-86946-44-3.
MORAVCOVÁ, Eva a kol. Cvičebnice pro předmět Operační výzkum A. Ostrava: EkF VŠB-Technická univerzita Ostrava, 2013. 134 s. ISBN 978-80-248-3066-7.
|
| Recommended Reading: |
|---|
TAHA, A. Operations Research: An Introduction (9th Edition) 832 p. Pearson 2010
|
HILLIER, Frederick S. and Gerald J. LIEBERMAN. Introduction to Operations Research. 9th ed. London: McGraw-Hill, 2009. 1088 pp. ISBN 978-80-077298340.
ŠUBRT, Tomáš a kol. Ekonomicko-matematické metody. Plzeň: Vydavatelství a nakladatelství Aleš Čeněk, 2011, 351 s. ISBN 978-80-7380-345-2.
ZONKOVÁ, Zdena a kol. Operační výzkum. 2. vyd. Ostrava: VŠB-TU Ostrava, 2002,
s. 217. ISBN 80-248-0190-6, 978-80-248-0190-2 (dotisk)
|
| Planned learning activities and teaching methods |
|---|
| Lectures, Tutorials |
| Assesment methods and criteria |
|---|
| Task Title | Task Type | Maximum Number of Points
(Act. for Subtasks) | Minimum Number of Points for Task Passing |
|---|
| Exercises evaluation and Examination | Credit and Examination | 100 (100) | 51 |
| Exercises evaluation | Credit | 45 (45) | 23 |
| Lineární programování | Written test | 25 | 13 |
| Síťová analýza | Written test | 15 | 8 |
| rychlotesty na cvičení | Other task type | 5 | 0 |
| Examination | Examination | 55 (55) | 28 |
| Written exam | Written examination | 55 | 28 |