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Mathematical Model for Faculty Budget
Holá, Lucie ; Roupec, Jan (referee) ; Popela, Pavel (advisor)
The idea of this diploma thesis is an origin application of optimization models to solve a wage funds allocation problem on various institutes of each faculty. This diploma thesis includes an outline of linear programming models, nonlinear programming models, multiply programming models and parametric programming models. Studied questions are debating in wider context of distributing financial resources from the Budget of the Czech republic, through Ministry of education, youth and sports, universities, faculties after as much as various institutes. The accent is given on question of definition assessment scales of achievement criteria with general-purpose kvantification.
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Modelling of the waste flow in the Czech Republic
Němcová, Lucie ; Procházka, Vít (referee) ; Šomplák, Radovan (advisor)
Strategic planning is the basis for efficient and sustainable waste management. Data collection and its deep understanding are essential for effective planning. Waste flows are an important information to assess waste management to date. This information has so far been available only aggregated at national level in the Czech Republic. In this thesis, an approach has been developed to reconstruct the waste flows at a sub-national level from available data. The approach consists of two optimization models: partial and final. The partial model is based on expert assumptions. The reconstruction of the flows by the partial model is done sequentially in smaller groups of flows. The computation of the partial model is repeated with different composition of the groups of flows optimized at the same time. Each iteration results in a~candidate solution which is used as an input data for the final model. The solution of the final model yields the final reconstruction of the waste flows. Model development and testing was carried out on problems simulated based on the real data from the waste management of the Czech Republic.
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New Trends in Stochastic Programming
Szabados, Viktor ; Kaňková, Vlasta (advisor) ; Lachout, Petr (referee)
Stochastic methods are present in our daily lives, especially when we need to make a decision based on uncertain events. In this thesis, we present basic approaches used in stochastic tasks. In the first chapter, we define the stochastic problem and introduce basic methods and tasks which are present in the literature. In the second chapter, we present various problems which are non-linearly dependent on the probability measure. Moreover, we introduce deterministic and non-deterministic multicriteria tasks. In the third chapter, we give an insight on the concept of stochastic dominance and we describe the methods that are used in tasks with multidimensional stochastic dominance. In the fourth chapter, we capitalize on the knowledge from chapters two and three and we try to solve the role of portfolio optimization on real data using different approaches. 1
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New Trends in Stochastic Programming
Szabados, Viktor ; Kaňková, Vlasta (advisor) ; Lachout, Petr (referee)
Stochastic methods are present in our daily lives, especially when we need to make a decision based on uncertain events. In this thesis, we present basic approaches used in stochastic tasks. In the first chapter, we define the stochastic problem and introduce basic methods and tasks which are present in the literature. In the second chapter, we present various problems which are non-linearly dependent on the probability measure. Moreover, we introduce deterministic and non-deterministic multicriteria tasks. In the third chapter, we give an insight on the concept of stochastic dominance and we describe the methods that are used in tasks with multidimensional stochastic dominance. In the fourth chapter, we capitalize on the knowledge from chapters two and three and we try to solve the role of portfolio optimization on real data using different approaches. 1
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Creation of equity portfolio under unusual market conditions by using the methods of decision making
Čižmař, Adam ; Borovička, Adam (advisor) ; Sokol, Ondřej (referee)
This bachelor thesis deals with problems of investing in stock market. There are plenty of different approaches to investing into stocks, however methods used in this thesis belong among multi-criteria decision making methods. Such an aproach is not commonly used which provides an interesting point of view that differs from widely used methods. This thesis consists of theoretical background to market environment and stocks themselves and also of theoretical description of multi-criteria evaluation and multi-criteria programming. Specifically I use ELECTRE I method as multi-criteria evaluation and aggregation of linear functions as multi-criteria programming method. By using these two methods I create two different portfolios based on two separate strategies. First of them aims to maximize capital gains whereas the second one aims to maximize dividend profits and to minimize risk, as well.
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High school timetabling using multicriteria linear programming
Žítek, Jan ; Skočdopolová, Veronika (advisor) ; Kuncová, Martina (referee)
The theme of this thesis is high school timetabling. The built mathematical model is based on bivalent programming. The model uses multicriteria linear programming too, because a timetable has to fill legal and school's requests and student's and teacher's wishes. Firstly, there are given theoretical basics. Then there is described economic model with school's characteristics and it continues by mathematical model. For optimization, tool MPL for Windows with using Gurobi. Finally, export of optimization is transferred using VBA to form for end users.
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Mathematical Model for Faculty Budget
Holá, Lucie ; Roupec, Jan (referee) ; Popela, Pavel (advisor)
The idea of this diploma thesis is an origin application of optimization models to solve a wage funds allocation problem on various institutes of each faculty. This diploma thesis includes an outline of linear programming models, nonlinear programming models, multiply programming models and parametric programming models. Studied questions are debating in wider context of distributing financial resources from the Budget of the Czech republic, through Ministry of education, youth and sports, universities, faculties after as much as various institutes. The accent is given on question of definition assessment scales of achievement criteria with general-purpose kvantification.
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Optimization of production of the nutritional products
Slámová, Dominika ; Sekničková, Jana (advisor) ; Kuncová, Martina (referee)
The theme of the thesis is to optimize the production of nutritional products of defunct company of Ing. Petra Němce. The company was engaged in production of nutritional mixtures for bakeries, pastry shops, ice cream parlours and gastronomy industry. The main objective is to create a model to find the optimal structure of production in order to maximize profit while minimizing costs and maximizing revenue. The partial task is to determine the optimum number of manufactured products and the quantity produced mixtures. The thesis describes particular solutions using the simplex method and integer linear programming. The compromise solution is obtained using multicriterial programming. Fulfilments of the set goals and their evaluation are described in the conclusion.
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Making an investment portfolio of unit trusts by using the fuzzy multiple criteria decision making methods
Borovička, Adam ; Fiala, Petr (advisor) ; Zornerová, Helena (referee) ; Pekár, Juraj (referee)
The thesis deals with investment decision making. It starts from the decision making situation about the making of an investment portfolio of the open unit trusts. The whole decision making process is described, namely the methodical approaches used in terms of the portfolio making procedure. Thus, the main part of this paper focuses on a detailed description of an algorithm of the fuzzy weight estimation method, fuzzy multiple criteria evaluation method and fuzzy multiple objective programming method. The methods are proposed on the basis of current concepts; they conclude the new ideas as well. The fuzzy weight estimation method is able to calculate the weights of criteria according to their linguistically expressed importance. The fuzzy multiple criteria evaluation method accepts uncertain input data in the form of the fuzzy numbers. The alternatives are evaluated by the concept of the preference relations. This method provides a division of the alternatives into the effective and ineffective. The fuzzy multiple objective programming method also works with the uncertain elements as fuzzy numbers. To solve the particular mathematical models, the Bellman's optimality approach is applied. The method is proposed in the interactive form. The decision maker can change a current solution by his/her additional (vague) preferences. The proposed concepts form the two-phase decision making procedure that is applied in the practical situation of the portfolio making in the field of the capital market with open unit trusts offered by the Česká spořitelna investment company. Two types of investors are defined, the investment situations are described, and the results are analyzed in detail. The decision making theory, the fuzzy sets theory and the capital market of collective investment, or with unit trusts, are introduced in a necessary scope. The instigation of my dissertation is to solve the real decision making situation. The investment decision making process is described and the methodical approaches are proposed in order to make the portfolio of unit trusts.
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Application of Methods of Decision Making Theory on Investments in Unit Trusts
Zikmundová, Alena ; Borovička, Adam (advisor) ; Kuncová, Martina (referee)
The aim of this paper is the application of decision making theory on setting up portfolios for model investors. In the first part, there is a brief overview of the topic of investment and capital market. In the second part, there is a description of the principals of multiple criteria evaluation of alternatives and multiple objective programming and the specific methods used in the paper are described. In the application, there are individual portfolios set up from stock, security and money market unit trusts in two phases. In the first phase, the weights for individual criteria are calculated based on the preferences of the investors and the effective alternatives are chosen using the Electre I method. In the second phase, the method of weighted sum of part objective functions is applied.
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