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Selected Advanced Stochastic Programming Models
Brzobohatý, Jan ; Hrabec, Dušan (referee) ; Popela, Pavel (advisor)
This diploma thesis deals with stochastic dominance. The goal is to lay the foundations for defining stochastic dominance, to describe its properties and to explain this concept on simple examples. Another goal is to apply this concept to network problems with random price. Examples in this thesis also contain solutions and python code how to find them.
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Optimal Scheduling Systems for Outdoor Activity
Rykala, Kryštof ; Matyáš, Jiří (referee) ; Češka, Milan (advisor)
The thesis discusses technologies and approaches for implementation of information system. Its part and motivation is automatic scheduling of activities. A model for resource-contraint project scheduling is defined using mixed-integer linear programming. Part of this thesis are client, server and planning programs that form a system for management of an outdoor center with automatic scheduling of activities.
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Selected financial optimization models
Bujnovský, Daniel ; Bednář, Josef (referee) ; Popela, Pavel (advisor)
This work is focused on models of optimal asset and liability management. The practical section illustrates various ways of modelling strategies depending on the problem formulation, chosen set of assets and the type of the used optimization technique. The main examples are portfolio immunization and the Yasuda-Kasai model together with the extended version of Markowitz model. The author provides across the work an overview of different financial risks and various tools for their measurement together with possible formulations of expected returns relevant to the studied models. The individual models are compared and often extended by other constraints in order to improve their practical applicability. From the point of view of the mathematical optimization several ways of input data generation are described for example by using the extended Brownian motion. All practical parts go hand in hand with illustrative pictures and codes. The necessary financial and mathematical theory is included as well.
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Selected Advanced Stochastic Programming Models
Brzobohatý, Jan ; Hrabec, Dušan (referee) ; Popela, Pavel (advisor)
This diploma thesis deals with stochastic dominance. The goal is to lay the foundations for defining stochastic dominance, to describe its properties and to explain this concept on simple examples. Another goal is to apply this concept to network problems with random price. Examples in this thesis also contain solutions and python code how to find them.
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Optimal Scheduling Systems for Outdoor Activity
Rykala, Kryštof ; Matyáš, Jiří (referee) ; Češka, Milan (advisor)
The thesis discusses technologies and approaches for implementation of information system. Its part and motivation is automatic scheduling of activities. A model for resource-contraint project scheduling is defined using mixed-integer linear programming. Part of this thesis are client, server and planning programs that form a system for management of an outdoor center with automatic scheduling of activities.
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Analysis of the performance growth of the optimization solvers
Škvarková, Alexandra ; Jablonský, Josef (advisor) ; Fábry, Jan (referee)
It would not be possible to solve real optimization problems, which usually contain a huge number of variables and constraints, without high-performance optimization systems. Today's software market offers a vast number of different systems available to provide solutions to linear and non-linear optimization tasks, including integer conditions. One such optimization system is called Gurobi. It is available in several versions. This thesis is focused on the performance comparison of three solver versions (i.e. 7.0.2, 6.0.5 and 5.0.2) using tasks that are in the MPS format, they are obtained from the MIPLIB 2010 electronic library, namely from the Benchmark section. The results are compared according to the time period needed to solve the task for each investigated version.
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