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Solving of integer problems by dynamic programming
Polonyankina, Tatiana ; Kalčevová, Jana (advisor) ; Lagová, Milada (referee)
Optimalization problems with integer requirements on the variables occurs in real life very often. Unfortunately, finding optimal solutions to such problems are often numerically very difficukt. The work describes several possible algorithms for solving linear integer problems. The reader is also familiarized with the method of dynamic programming and the principle of optimality. This is demonstrated in a practical example of a knapsack model where the calculation is done using tables. The goal of this work is to apply the knowledge from the application of dynamic programming on a typical linear integer problems, namely on the problem of material separation, and thus show the algorithm of calculating integer problems. Finding the optimal integer solution is accomplished in two ways: by the classical method of spreadsheet tables and by the simplified method of using Lagrange multipliers. In the conclusion there are summarized the advantages and disadvantages of solving technic.
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The Asymptotic Integer Algorithm
Murinová, Michaela ; Kalčevová, Jana (advisor) ; Jablonský, Josef (referee)
This work is dealing with the tasks of integer programming and with the methods for their solving. The most famous methods are "branch and bounds method" and the Gomory's method of cut algorithms. The purpose of this work is to get readers acquainted with the alternative method of asymptotic integer algorithm. This method is based on the similar idea as the rounding procedure. The main idea is to enable the nonbasic variables gain a non-zero value. It leads to cutting the continuous (noninteger) solution space on the graphics illustration, while no integer solution should be lost. This method is presented on the example, which is a part of the main chapter and furthermore on its own example in the third chapter.
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Evaluation of territories from the perspective of multicriteria decision making
Vondrušková, Hana ; Kalčevová, Jana (advisor) ; Kuncová, Martina (referee)
This diploma thesis deals with selecting the best places to live from the student perspective, the University of Economics, Prague. The paper briefly describes methods of multicriteria decision making. Selected methods (ELECTRE III, PROMETHEE II, WSA, TOPSIS and ORESTE) are then used to assess regions of the Czech Republic. This role is based on real data of the Czech Republic region and the students' preferences regarding place of residence. Information about the preferences of students was obtained by questionnaire survey of students of the University of Economics, Prague. Data processing was used in addition to MS Excel - Sanna.
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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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The Generalized Distribution Problem Approach
Fuksová, Lucie ; Lagová, Milada (advisor) ; Kalčevová, Jana (referee)
The generalized distribution problem is task from linear programming approach which belongs to the distribution problems with specific mathematical model. For solution this problems we need to use another methods than the universal simplex method. A typical example is the transportation problem. The generalized distribution problem differs from it only in a small difference in mathematical model, but compared to the traffic problem has computational difficulties. To build the model and its solution is necessary to calculate the transmission coefficients, the so-called "performance factors". This work will prepare the answers for problem formulations and mathematical model and will describe the procedures that can solve problems of similar type. Methods used in the thesis are modified distribution method and the simplex method. To calculate solutions will be used the optimization software Lingo.
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Generation of linear programming tasks
Serbová, Eva ; Lagová, Milada (advisor) ; Kalčevová, Jana (referee)
Bachelor thesis deals with generation of linear programming (LP) tasks for academic education purposes. In the beginning part of thesis there are briefly described methods for pseudorandom numbers generation and basic characteristics of linear programming methods. Chosen and realised procedure of LP tasks generation is based on inverse algorithm. Inverse algorithm proceeds from resultant values backward to input ones. This process provides generation of LP tasks. All tasks are comparable in terms to calculation difficulty. This method is appropriate for manual calculating and is suitable for practicing and testing of students. Part of the text contains brief description of the application program LinPro which is used successfully in education of lessons accredited by Department of Econometrics at University of Economics in Prague. The thesis is finished by couple of sample models.
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Multiobjective portfolio analysis
Kunt, Tomáš ; Kalčevová, Jana (advisor) ; Kuncová, Martina (referee)
The objective of this thesis is to apply alternative multi-objective optimization techniques to the portfolio selection problem. Theoretical part starts with detailed analysis of the classical Markowitz model and its assumptions. Following that, introduction of multi-criterion optimization techniques available for finding non-dominated portfolios is given. One of these techniques, the genetic algorithm, is presented in great detail. Some of the basic methods useful for predicting stock prices and its risks are presented at the end of the theoretical part. Practical part presents an application of the theory to the problem of constructing efficient portfolios of 11 selected stocks traded on Prague Stock Exchange. Results achieved by different approaches are compared and interpreted.
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Financial optimization
Štolc, Zdeněk ; Kuncová, Martina (advisor) ; Kalčevová, Jana (referee)
This thesis is focused on a theoretical explanation of some models for the optimization stock portfolios with different risk measure. The theory of the nonlinear programming is detailed developed and also basic Markowitz`s model with another optimization models as Konno -- Yamazaki`s model, Roy`s model, semivariance approach and Value at Risk approach, which are based on alternative risk measure. For all models the assumptions of their applications are highlighted and the comparation of these models is made too. Analytical part is concerned in the construction of the effecient portfolios according to the described models is made on the historical market prices of 13 companies traded on Prague Stock Exchange in SPAD.
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