
Algorithms for solving of special knapsack problems and their computational complexity
Sem, Štěpán ; Ivánek, Jiří (advisor) ; Kalčevová, Jana (referee)
The thesis deals with knapsack problems variants and possibility of their solving, furthermore with the impact of particular task (instance) special structure on the effciency of tested approach. The thesis also proposes conversion possibility between described tasks and their continuous extension (continuous relaxation). It describes L3 algorithm and superdecreasing knapsack problem solving from the common sort of algorithms and Monte Carlo Method, simulated annealing and genetic algorithms from the sort of probability ones. Other possibilities are also discussed. Integral part of this thesis is the accompanying application, which was used to create groundwork used in the text and which can be also used to solve other instances.


Optimizing the use of agricultural areas  a case study
Jirků, Šárka ; Kuncová, Martina (advisor) ; Kalčevová, Jana (referee)
This study deals with analysis of the agricultural company layout. The utilization of agricultural areas is optimized with such a sowing technique that leads to the highest harvest profit. All these issues are being solved by the conversion to the linear programming model which is the most resembling to the combination of production planning and allocation problem. A case study is based on actual data given by Agrofarma Týnec, s.r.o. company. The 48 sections of field in different proportion are taken in consideration as well as five different crops. The study tries to deal with more options taking in account different trade prices of set commodities and a hectare sowing limitation. The main model anticipates pessimistic trade prices expectations and does not restrict hectare sowing with single crops. The model is followed by the price coefficient analysis that gives the price level to be kept to let the computed solution be optimal. Lingo13.0 was used as an optimization software.

 

An analysis of the results of Parliamentary Elections in the Czech Republic
Kopecká, Barbora ; Kalčevová, Jana (advisor) ; Kuncová, Martina (referee)
The election to the Chamber of Deputies of the Parliament of the Czech Republic took place in 2010. The theses focuses on examining of preelection polls and election results themselves using some knowledge of game theory and public choice theory. The work describes in detail the methodology of processing election results as it works in the Czech Republic at present. Preelection polls of selected survey agencies are compared and evaluated here. Further the theses uses an alternative approach to the distribution of seats in the Chamber of Deputies, with a focus on possible impact on the election results both in terms of the different distribution of seats, and in terms of the subsequent formation of possible coalitions. There are also discussed all possible coalitions which were suggested after the elections in 2010.


Econometric Analysis of Microeconomic Processes. Application on Wages in the Czech Republic
Kalčevová, Jana ; Pánková, Václava (advisor) ; Arlt, Josef (referee) ; Cahlík, Tomáš (referee)
This thesis is focused on wages models on the czech labor market in 1996 and 2002. Wages models are built on nontrivial mathematical background and parameters of given models are estimated by methods based on sum of squared residuals and also not often used quantile regression. The quantile regression theory is described in the thesis together with test statistics. Properties of estimations, demonstration examples and proposal of practical application are also indroduced. The theory was applied to two largesize datafiles, recieved results show the difference between years 1996 and 2002; a comparison with European Union countries is also given.


Alternative Method of Solution for LP Problem
Hanzlík, Tomáš ; Kalčevová, Jana (advisor) ; Rada, Miroslav (referee)
Linear programming (LP) stands for an optimization of a linear objective function, subject to linear and nonnegativity constraints. For this purpose many methods for LP emerged. The best known is Simplex Method. Another group of methods for LP is represented by Interior Point Methods (IPM). These methods are based on interior points of feasible region of a problem, while Simplex Method uses basic feasible solution of a problem. This thesis focuses on theoretical background of IPM and brings it into relation with algorithms based on IPM. KKT system and its significance are included and the algorithm solving Linear Complementarity Problem is discussed as well. In this thesis, two algorithms based on IPM are introduced and used for solving a sample LP problem.


Alternative rules for determining pivot columns and pivot rows in the simplex method
Leontiev, Andrey ; Kalčevová, Jana (advisor) ; Skočdopolová, Veronika (referee)
In my thesis I tried to describe the problems of choice of a pivot in the simplex method. The first part is devoted to the mathematical model of linear programming and simplex method in general. Here are explained the key concepts and principles of this method. There is the description of alternative rules for choosing a pivot using the simplex method in the second part. The description of each method is supported by example. I emphasize here the proofs of finite algorithm for each rule. In the last part of my thesis I have placed my own examples to show the different effects using different methods.


MultiCriteria Decision Making in Data Envelopment Analysis
Mec, Martin ; Jablonský, Josef (advisor) ; Kalčevová, Jana (referee)
Data Envelopment Analysis is a multicriteria decision making tool employing set of minimizing criteria (inputs) and set of maximizing criteria (outputs) for evaluating decision making unit efficiency. This method is accompanied by problems in field of input and output weight assignment, whereas benevolent basic model formulation enables decision making unit evaluation to be based on far unevenly distributed weight vector. Furthermore, data envelopment analysis basic model produces dichotomized dividing in form of efficient and inefficient decision making unit sets. Extensive set of efficient units occurs frequently and this causes difficulties in choosing one or less number efficient units. These phenomena appear often simultaneously. An implementation of multicriteria decision making models into data envelopment analysis is exercised in order to reduce these undesired effects in applications.


Systém pro řešení úloh vícekriteriálního hodnocení variant v prostředí internetu
Zavrtálek, Jan ; Jablonský, Josef (advisor) ; Kalčevová, Jana (referee)
This diploma thesis deals with description of methods and original online application for solving multicriteria evaluation of alternatives problems. Methods based on maximisation of utility value (WSA), minimisation of distance from ideal alternative (TOPSIS), evaluation of preference relations (ELECTRE) and evaluation along preference flows (PROMETHEE) are described and implemented in the application. The thesis introduces an original web application written in PHP language which is developed for solving multicriteria evaluation of alternatives problems in internet environment. The application running on webserver allows solving multicriteria evaluation of alternatives problems by four above mentioned methods. The application is controlled by any web browser. A runtime complexity of used algorithms is measured and discussed.


Optimal composition of groceries for mountain trip
Fesenko, Anastasiya ; Kalčevová, Jana (advisor) ; Flusserová, Lenka (referee)
This work is aimed towards the application of knapsack problem in practical example of packing of groceries for mountain trip. The knapsack problem is one of the tasks of integral programming; those are the models that can only variably accept the integral value. The solutions of integral tasks are usually very meticulous. That is why for their solution special algorithms were created, which are capable of discovering an integral solution of such tasks, for example, branch and bound method, Balas method etc. These types of algorithms are defined in the first part of this work. While writing this thesis a considerable emphasis was put into application of its result in practice. Hence, for achieving applicability practical tasks are solved from various angles and therefore various aims have been set forth in each solution option. The results of each option are interpreted and then the differences are explained.
