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Multiobjective portfolio optimization
Malá, Alena ; Kopa, Miloš (advisor) ; Dupačová, Jitka (referee)
The goal of this thesis is to summarize three basic principles of solving multi-objective programming problems. We focus on three approaches: a linear combination of objective functions, ε-constrained approach and a goal programming. All these methods are subsequently applied to US data. We consider monthly excess returns of ten US representative portfolios based on individual stock market capitalization of equity that serve as basic assets. Our aim is to find the efficient portfolios. Next we investigate a structure of these portfolios and their mutual relationships. Graphic representation of efficient frontiers is also included in the thesis. All calculations were performed using Mathematica software version 8.
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The Optimalization of Capacity Menu
Achimovič, Peter ; Skočdopolová, Veronika (advisor) ; Dlouhá, Zuzana (referee)
The bachelor work is aimed of the composition of capacity menu for young trainees, who want to increase their actual physical form through healthy diet with all of basic macronutrients and they dispose of limited financial budget, as well. The work is systematically structured of four sections, the first part is concerned with definitions of essential terms of linear programming with their metodology. The second part presents fundamental knowledge of nutrion, characteristic of somatotypes and relevant value of components in food.. The main aim of the work is creation of capacity menu through linear and goal programmnig, which are explained in practical part of third and fourth section. Constructed mathematical model is solved in optimalization software LINGO and MS Excel. The interpretation and evaluation of the work is described in coclusion.
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Practical use of diet problem
Vítek, Lukáš ; Kuncová, Martina (advisor) ; Sekničková, Jana (referee)
The aim of this bachelor thesis is to formulate a mathematical model of linear programming problem, which will optimize the menu composition based on a required optimal amount of macronutrients. The goal programming approach is used to solve this problem. At first, the model which will only optimize diet with respect to nutritional values is formulated. After that this model is modified to provide a practically usable menu composition. Finally, the model is upgraded to three days model and more alternative ways are used to solve the problem. There is introduced theory of operational research and linear programming and basic recommendations on a balanced diet in the beginning of the thesis. Then these theoretical knowledges are used in a practical part. All models are formulated in MPL for Windows and solved by the solver Gurobi. The foodstuff database was created in the Microsoft Excel.
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Scenario generation by the moment fitting method
Koláčková, Hana ; Dupačová, Jitka (advisor) ; Branda, Martin (referee)
The thesis presents four methods for scenario generating leading to the resulting discrete probability distribution that replicates given values of the moments. The first method uses heuristic algorithm, the second method generates by symmetrically distributing values around the mean value, the third one is based on solving the system of nonlinear equations and finally the last method is based on goal programming. Next section describes the nature of problems solved by the goal programming. It also details possible ways of parameter specification to allow control of the computational complexity. In the last part of the thesis the results of several suitable methods for chosen types of problem are compared. Powered by TCPDF (www.tcpdf.org)
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Multiobjective portfolio optimization
Malá, Alena ; Kopa, Miloš (advisor) ; Dupačová, Jitka (referee)
The goal of this thesis is to summarize three basic principles of solving multi-objective programming problems. We focus on three approaches: a linear combination of objective functions, ε-constrained approach and a goal programming. All these methods are subsequently applied to US data. We consider monthly excess returns of ten US representative portfolios based on individual stock market capitalization of equity that serve as basic assets. Our aim is to find the efficient portfolios. Next we investigate a structure of these portfolios and their mutual relationships. Graphic representation of efficient frontiers is also included in the thesis. All calculations were performed using Mathematica software version 8.
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Goal Programming Models: Theory, Applications, Software Support
Skočdopolová, Veronika ; Jablonský, Josef (advisor) ; Brezina, Ivan (referee) ; Šubrt, Tomáš (referee)
Goal programming is an approach for solving decision problems. The aim of this doctoral thesis is to show the practical use of this approach for solving real problems. The first chapter brings a brief introduction to multicriteria decision making. The second chapter is devoted to goal programming, its history, theory, criticism and also to its practical applications. The third chapter deals with description of a model for optimisation of white mass production. This model utilises the goal programming principle to deal with measuring deviations of raw materials' composition. A part of this chapter is a presentation of OPTIPROT, an application that implements the mentioned model. In the fourth chapter there are described three mathematical models for timetabling at a department level; two multistage models and one complex model. All three models are formulated utilising goal programming. In this chapter there is also described an application that implements the complex model for timetabling.
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Planning a holidays in Europe with using goal programming
Otarbayeva, Zhamilya ; Skočdopolová, Veronika (advisor) ; Kuncová, Martina (referee)
In this thesis I consider possibility to spend my vacation in one of the three countries: Spain, France, Italy. In each country I chose ten cities, which I would like to visit. I will use Travel Salesman Problem to decide the best route inside each country according to three criteria: Cost, Minutes and Transport. There is also a possibility to choose the type of transport: train or combination of train and airplane. Also I will use Weighted goal programming and Chebyshev goal programming to optimize all criteria simultaneously. In the end I will use multiple -- criteria decision analysis to compare results. According to three methods (ORESTE, ELECTRE III, TOPSIS) I will choose one of the states for my vacation. I will make all calculation in program MPL and in Excel using solver SANNA.
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Optimization of children food at the camp
Kadlecová, Kateřina ; Skočdopolová, Veronika (advisor) ; Kobzareva, Maria (referee)
This bachelor's thesis focuses on a diet optimization of the children's summer camp cuisine in accordance with the standards placed on the nutritional food composition as well as on the equipment and possibilities of the local kitchen. The theoretical part of the thesis includes the description and the structure of the operational research problem. Whereas the aim of the empirical part was to model the problem as a task of the linear as well as the goal programming. Both these tasks were solved in the LINGO software. The results were exported into MS Excel and then added to the text of the present thesis as the tables of resulting menus. The present thesis identifies the nutritional value and composition of 43 dishes. The list of these dishes served as the input file used for the modelations mentioned above.
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Models of goal programming and their application
Nguyen, Anh Vu ; Jablonský, Josef (advisor) ; Skočdopolová, Veronika (referee)
The aim of this thesis is to make a model of a goal programming and to show its usage on practical examples. The goal programming is the most frequent method of searching for compromise solution to task of multi-criteria programming so that's why at the begenning of this thesis these methods are described with various ways of searching for compromise solution. The second chapter deals with the goal programming.Furthermore, based on a concrete example is showed the procedure of solving the decision problem using the goal programming model and linear programming model. The fourth chapter is about optimalisation system LIONGO, which can be used to solve the goal programming problems.
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The Optimalization of diet composition with the use of goal programming
Hrubá, Lucie ; Skočdopolová, Veronika (advisor) ; Kuncová, Martina (referee)
The nutritive problem is characteristic task for linear programming whose role is to propose daily dose of nutrients in nourishment. The goal is to set up balanced menu for the individual person. Goal programming is used in case when is not necessary to have exact restricted conditions. The conditions are set up so final value is getting closer to assigned value that is target value. In this work will be goal programming utilized for model modification of the nutritive problem. For the nutritive problem is possible to use goal programming so particular limitation of nutrients level in nourishment will not be restricted rigorously in a form of inequalities, but so that final value is getting closer either from the top or from the bellow target value. Firstly will be created the model for linear programming with minimum costs following the model with goal programming and after that comparison will be done.
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