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Generalisation of Cournot oligopoly model for more players
Nehasil, Václav ; Chrobok, Viktor (advisor) ; Zouharová, Martina (referee)
This thesis deals with oligopolistic market and situations occurring in it. Its aim is to approximate basic principles and rules, which relate to oligopoly. Thesis is limited to the situation when the products of all firms are homogeneous and these firms compete only by the produced quantities. Models of Cournot and Stackelberg are introduced in it. The possibilities of cooperation are being researched using the theory of games. Solved mathematical problem is attached to each of these models and it demonstrates all the procedures properly. Derivation of general formulas, if all cost and price functions are linear, is located in the second part of the thesis. Their utilization is demonstrated on solved mathematical problem and verification of them is located there.
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A Selection of Optimal Portfolio by Multiple-Criteria Decision Making
Jančíková, Denisa ; Borovička, Adam (advisor) ; Zouharová, Martina (referee)
This bachelor thesis deals portfolio optimization mainly by multiple-criteria decision making. First part is using linear programming to generate five different investment portfolios that are focusing on one criterion. Then I selected the best portfolio using TOPSIS method in regard to all criterions. Before that it is important to introduce linear programming. It is followed with summary of multi-criteria evaluation of alternatives, method of determining weight of individual criterions and introduction to portfolio theory. It is fundamental to mention all the relevant characteristics of Prague Stock Exchange. All companies that are included in this work are shortly introduced. The final output contains overall summary of results and recommendations for investor.
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System for solving distribution problems of LP – LINGO/Excel interface
Krčál, Adam ; Jablonský, Josef (advisor) ; Zouharová, Martina (referee)
Discrete problems of linear programming, i. e. problems with integer or binary variables, have a great amount of real-life applications. Among distribution problems, belong many different kinds of problems with discrete character -- transportation problem, container transportation problem, allocation problem, assignment problem, plant location problem, traveling salesman problem etc. In this work the theoretical aspects of chosen types of problems are explained and then an application in Microsoft Excel 2010 environment is created. For that purpose programming language VBA is the key instrument. The application cooperates with two different optimization systems -- the Solver add-in in Excel and professional optimization system Lingo. Functionality of the application is thereafter tested on some examples.
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Optimization of Algae Population Growth Using Markov Chains and
Zouharová, Martina ; Kalčevová, Jana (advisor) ; Černý, Michal (referee)
The thesis deals with the task of refining the constructional and operational parameters of a tubular photobioreactor in order to maximise the growth rate of algae contained in the cultivation suspension. It builds on a basic growth model of the Porhydrium sp. alga, and focuses on the optimization of external irradiance, which is one of the key determinants of algae growth. Two distinct methodological approaches are applied: analytic approach, which employs Markov Chains, and simulation approach, which relies on agent-based simulations. In the analytic part, we introduce the construction of state transition matrix for a Markov Chain that accounts for varying irradiance inside the photobioreactor (in contrast to constant-irradiance methods that have been published so far). In the simulation part, we devised an agent-based model of algae population that enables us to analyze the system behaviour while interactively changing the model parameters. In the context of the results from both the analytic and simulation part, we conclude by suggesting the optimal level of external irradiance.
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