| Course Unit Code | 157-0372/02 |
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| Number of ECTS Credits Allocated | 5 ECTS credits |
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| Type of Course Unit * | Compulsory |
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| Level of Course Unit * | Second Cycle |
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| Year of Study * | First Year |
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| Semester when the Course Unit is delivered | Summer Semester |
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| Mode of Delivery | Face-to-face |
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| Language of Instruction | Czech |
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| Prerequisites and Co-Requisites | Course succeeds to compulsory courses of previous semester |
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| Name of Lecturer(s) | Personal ID | Name |
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| ZAP149 | doc. Mgr. Ing. František Zapletal, Ph.D. |
| CHY0034 | Mgr. Ing. Lucie Chytilová, Ph.D. |
| TOL0013 | prof. Mehdi Toloo, Ph.D. |
| Summary |
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| Students learn both the theoretical background and possibilities of applications in practice. They will get know how to define a mathematical optimization model when risk (stochastic programming) and uncertainty (fuzzy programming) are involved and how to solve these models using software (Solver, GAMS). |
| Learning Outcomes of the Course Unit |
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| The aim of the course is to present advanced optimization methods to students. In particular, an emphasis is put on optimization under risk and uncertainty and efficiency evaluation. |
| Course Contents |
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1. Linear programming (model, solution, duality).
2. Necessary and sufficient conditions of optima (KKT conditions), Trap of local optima).
3. Risk - random variables and its description.
4. Stochastic programming - introduction, classification.
5. Stochastic programming - single-stage models, chance constraints.
6. Stochastic programming - two-stage models (models with recourse), multi-stage models.
7. Stochastic programming - mean-risk portfolio models.
8. Introduction to fuzzy sets, logic and algebra.
9. Fuzzy programming - selected defuzzification measures, alpha-cuts, possibilistic programming.
10. Fuzzy programming - flexible programming models.
11. Data Envelopment Analysis (DEA) - introduction.
12. Data Envelopment Analysis (DEA) - CCR and BCC model.
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| Recommended or Required Reading |
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| Required Reading: |
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SHAPIRO, Alexander, RUSZCZYNSKI, Andrzej a Darinka DENTCHEVA. Lectures on Stochastic Programming: Modeling and Theory, 2009. ISBN 978-0-89871-687-0.
FIEDLER, Miroslav a kol. Linear optimization problems with inexact data. New York: Springer, 2006. ISBN 0-387-32697-9.
PRÉKOPA, András. Stochastic programming. Dordrecht: Kluwer Academic Publishers, c1995. Mathematics and its applications, v. 324. ISBN 0-7923-3482-5. |
SHAPIRO, Alexander, RUSZCZYNSKI, Andrzej a Darinka DENTCHEVA. Lectures on Stochastic Programming: Modeling and Theory, 2009. ISBN 978-0-89871-687-0.
FIEDLER, Miroslav a kol. Linear optimization problems with inexact data. New York: Springer, 2006. ISBN 0-387-32697-9.
JABLONSKÝ, Josef a Martin DLOUHÝ. Modely hodnocení efektivnosti produkčních jednotek. Professional Publishing, Praha, 2004. ISBN 80-86419-49-5.
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| Recommended Reading: |
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TAHA, Hamdy A. Operations research: an introduction. 9. vyd. International ed. Upper Saddle River: Pearson, 2011. ISBN 978-0-13-139199-4.
SHAPIRO, Alexander a Andrzej RUSZCZYŃSKI, ed. Stochastic programming. Amsterdam: Elsevier, 2003. Handbooks in operations research and management science, v. 10. ISBN 0-444-50854-6.
VLACH, Milan a Jaroslav RAMÍK. Generalized concavity in fuzzy optimization and decision analysis. Boston: Kluwer Academic Publishers, c2002. International series in operations research & management science, 41. ISBN 0-7923-7495-9. |
ZMEŠKAL, Zdeně, DLUHOŠOVÁ, Dana a Tomáš TICHÝ. Finanční modely: koncepty, metody, aplikace. 3., přeprac. a rozš. vyd. Praha: Ekopress, 2013. ISBN 978-80-86929-91-0.
NOVÁK, Vilém. Základy fuzzy modelování. Praha: BEN - technická literatura, 2000. ISBN 80-7300-009-1.
TAHA, Hamdy A. Operations research: an introduction. 9. vyd. International ed. Upper Saddle River: Pearson, 2011. ISBN 978-0-13-139199-4.
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| Planned learning activities and teaching methods |
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| Lectures, Tutorials |
| Assesment methods and criteria |
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| Task Title | Task Type | Maximum Number of Points
(Act. for Subtasks) | Minimum Number of Points for Task Passing |
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| Credit | Credit | 45 (45) | 23 |
| Stochastické a fuzzy programování | Written test | 30 | 15 |
| Written project - application of DEA methods | Semestral project | 15 | 7 |