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Methods for ranking efficient units in data envelopment analysis
Gőtz, Ondřej ; Jablonský, Josef (advisor) ; Chrobok, Viktor (referee)
This thesis focuses on the theory of models, data envelopment analysis and subsequent methods in ranking of obtained efficient units. The thesis is divided into three main parts. The first part describes the basic theoretical background of data envelopment analysis for different situations of inputs and outputs. It also contains basic information on specific models of CCR, BCC and SBM, including illustrative examples of their function. In the second part these models are adapted for use in the overall layout of production units which are the models of super efficiency and cross efficiency. Both methods include the description of the basic principles of their functioning. The aim is to compare the results of the various types of ranking using a practical example. This is included in the last part of the thesis. This chapter compares the results obtained using the models mentioned above. Data of the S & L branches were used as the input values for this work.
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Price of Volatility of Financials Assets
Gříšek, Lukáš ; Černý, Michal (advisor) ; Chrobok, Viktor (referee)
This diploma thesis describes problem of change-points in volatility of the time-series and their impact on price of nancial assets. Those change-points are estimated by using statistical methods and tests. Change-point estimation was tested on simulated datas and real world driven datas. Simulation helped to discover signi cant characteristics of change-point test, those data were simulated with using stochastic calculus. Google share prices and prices of call options were chosen to analyse impact of volatility change on those prices. Also implied volatility and its impact to call option price was analysed.
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RBC model - application to the Czech Republic
Báča, Petr ; Pánková, Václava (advisor) ; Chrobok, Viktor (referee)
The diploma thesis deals with the basic Real Business Cycle (RBC) model. RBC theory provides pure supply-side explanation of economic fluctuations. Generaly acknowledged contribution of RBC theory is the fact that the model is developed strictly on microeconomic basis. The thesis consists of two basic parts, theoretical and practical. First, historical background of RBC theory is mentioned. Then the basic RBC model is step-by-step derived and all equations are provided with explanations. In the last theoretical part section RBC theory critisism is discussed. In the practical part the derived basic model is applied to the Czech economy. First certain properties of the Czech business cycles are examined. Then, the basic model is calibrated, simulated and the results are commented.
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Optimization in systems of biological populations
Hašek, Pavel ; Chrobok, Viktor (advisor) ; Černý, Michal (referee)
This paper deals with optimization in systems of biological populations adjusted to harvesting. First, a description, behavior and evolution over time in basic models of Malthus, Verhulst and Gompertz, is solved in case of not harvesting and then harvesting. There are two options for harvesting, continuous and discrete harvesting. In case of continuous harvesting we have two ways how to harvest,with constant yield and constant effort. With simplifying assumptions it is possible to combine continuous and discrete model in the form of profit function for the harvesting and also gives us ability to implement harvesting costs. For profit-seeking function is best solved using numerical methods with model examples with help of the Maple solver. The last chapter is devoted to the introduction of interest to the harvesting models.
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Evaluation and decomposition efficiency using Malmquist productivity index
Skočdopol, Petr ; Dlouhý, Martin (advisor) ; Chrobok, Viktor (referee)
At first, the basics of microeconomics from the perspective of companies, effectiveness and methods of its measurement and the most important information on the distance function this thesis, are shown. It also contains the development of the Malmquist productivity index. The aim of this work is the description of this index and its components. Indicate how these values are calculated and what expressed. Secondary objectives are to introduce different variants of Malmquist indexes and their use. Four models are used for calculating individual components of the Malmquist productivity index. These are the DEA models, Aigner-Chu, Stochastic production frontiers and Stochastic activity analysis. The first three in this work are described in detail. In conclusion is an illustrative example of calculation Malmquist productivity index using DEA models. For the calculation I used the program Lingo.
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Sudoku - formulation and solving the problem
Jelínek, Tomáš ; Jablonský, Josef (advisor) ; Chrobok, Viktor (referee)
This bachelor thesis deal with the Sudoku game, there are delevoped models for solving the Sudoku and model for problem generation. There are described the rules of the game, history and some possible modifications in the first chapters. Models are developed in environment Xpress-IVE, there are described some of its features. Models for solving the Sudoku are being used two approaches - linear programming and constraint programming. Both methods are described, there are made mathematical models, which are then re-written in Mosel language. There are used both methods in model for problem generation, algorithm works on principle, where numbers are gradually removed from full Sudoku table.
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Application of data envelopment analysis to the efficiency assesment of bank branches
Vavruška, Marek ; Jablonský, Josef (advisor) ; Chrobok, Viktor (referee)
In the first, theoretical part of this bachelor thesis the theoretical basis of data envelopment analysis (focusing on the CCR and BCC models) is described and its principle is illustrated with the simple examples. The aim of this thesis is to analyze the efficiency of GE Money Bank branches, using the models described in the first part. The choice of inputs and outputs of bank branches is based on foreign studies, referred to in the second part. Another goal is the inclusion of the factor of potential of bank branches, which is understood here as the average gross wage in the given region. This was achieved by the modification of original data using the ratio of average gross monthly wage in the Czech republic and the average gross monthly wage in the given region. There are compared the results obtained by a calculation based on the original data and the results achieved after adjusting the data, in the final part of the thesis.
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Těžba v Predator-Prey modelu
Chrobok, Viktor ; Lagová, Milada (advisor) ; Kalčevová, Jana (referee)
The paper is focused on the Predator-Prey model modified in the case of harvesting one or both populations. Firstly there is given a short description of the basic model and the sensitivity analysis. The first essential modification is percentage harvesting. This model could be easily converted to the basic one using a substitution. The next modification is constant harvesting. Solving this system requires linearization, which was properly done and brought valuable results applicable even for the basic or the percentage harvesting model. The next chapter describes regulation models, which could be used especially in applying environmental policies. All reasonable regulation models are shown after distinguishing between discrete and continuous harvesting. The last chapter contains an algorithm for maximizing the profit of a harvester using econometrical modelling tools.
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