Gurantor department | Department of Systems Engineering | Credits | 5 |

Subject guarantor | prof. Ing. Jana Hančlová, CSc. | Subject version guarantor | doc. Mgr. Ing. František Zapletal, Ph.D. |

Study level | undergraduate or graduate | Requirement | Compulsory |

Year | 2 | Semester | summer |

Study language | English | ||

Year of introduction | 2019/2020 | Year of cancellation | |

Intended for the faculties | EKF | Intended for study types | Bachelor |

Instruction secured by | |||
---|---|---|---|

Login | Name | Tuitor | Teacher giving lectures |

HAN60 | prof. Ing. Jana Hančlová, CSc. | ||

ZAP149 | doc. Mgr. Ing. František Zapletal, Ph.D. |

Extent of instruction for forms of study | ||
---|---|---|

Form of study | Way of compl. | Extent |

Full-time | Credit and Examination | 2+2 |

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.

Lectures

Tutorials

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.

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.

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.

Credit - linear programming + network analysis + quick test during semester
Exam - combined (test + oral exam)

LMS Moodle

Credit - linear programming + network analysis + quick test during semester
Exam - combined (test + oral exam)

Subject code | Abbreviation | Title | Requirement |
---|---|---|---|

151-0500 | Math A | Mathematics A | Compulsory |

Subject has no co-requisities.

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.

Task name | Type of task | Max. number of points
(act. for subtasks) | Min. number of points |
---|---|---|---|

Credit and Examination | Credit and Examination | 100 (100) | 51 |

Credit | Credit | 45 (45) | 23 |

zápočtový test LP | Written test | 25 | 13 |

Zápočtový test SA | Written test | 15 | 8 |

Rychlotesty na cvičeních | Other task type | 5 | 0 |

Examination | Examination | 55 | 28 |

Show history

Academic year | Programme | Field of study | Spec. | Zaměření | Form | Study language | Tut. centre | Year | W | S | Type of duty | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

2020/2021 | (B0311A050005) Applied Economics | (S02) International Economic Relations | P | English | Ostrava | 2 | Compulsory | study plan | ||||

2020/2021 | (B0311A050005) Applied Economics | (S01) Economic Development | P | English | Ostrava | 3 | Compulsory | study plan | ||||

2020/2021 | (B0412A050006) Finance | P | English | Ostrava | 2 | Compulsory | study plan | |||||

2019/2020 | (B0311A050005) Applied Economics | (S02) International Economic Relations | P | English | Ostrava | 2 | Compulsory | study plan | ||||

2019/2020 | (B0311A050005) Applied Economics | (S01) Economic Development | P | English | Ostrava | 3 | Compulsory | study plan | ||||

2019/2020 | (B0412A050006) Finance | P | English | Ostrava | 2 | Compulsory | study plan |

Block name | Academic year | Form of study | Study language | Year | W | S | Type of block | Block owner |
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