
Network simplex method
Khýr, Lukáš ; Janošťák, František (referee) ; Popela, Pavel (advisor)
This thesis is focused on summary knowledges relating to mathematical modeling in optimization area. We will deal with simplex method in detail and especially its network modification, which is used in various practical applications. We will solve tasks of various sizes and compare their solutions using implementation these two methods in Matlab. There is solved a task with real data provided by the Institute of Process Engineering at the end of the work.

 
 

Implemenation of a Game Theory Library
Židek, Stanislav ; Peringer, Petr (referee) ; Hrubý, Martin (advisor)
Game theory has become very powerful tool for modelling decisionmaking situations of rational players. However, practical applications are strongly limited by the size of particular game, which is connected to the computational power of computers nowadays. Aim of this master's thesis is to design and implement a library, which would be able to find correlated equilibria in as complex noncooperative games as possible.


Origin of linear programming as a scientific discipline
Fišmon, Petr ; Šindelářová, Irena (advisor) ; Kuncová, Martina (referee)
This thesis deals with the origin and extension of linear programming. It describes various influences that have participated in its formation. The first part of thesis describes military influences, which stimulated governments of great powers to support mathematical modelling and development of linear programming. Next point of the bachelor paper is development of general linear model that was based on economics models. The thesis deals with mathematic theory, which gave the foundation to the Simplex method and with computer technology, which was able to solve linear models and put them into practice.


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.


Analysis of reduced and shadow prices in linear programming problems with lower and upper bounds
Průšová, Lucie ; Jablonský, Josef (advisor) ; Kořenář, Václav (referee)
Abstract Title: Analysis of reduced and shadow prices in linear programming problems with lower and upper bounds. Author: Lucie Průšová Department: Department of Econometrics Supervisor: doc. Ing. Milada Lagová, CSc. This thesis deals with linear programming problems with additional requirements that values of variables are greater or lower than a specified bound. Where applicable, the variable is limited on both sides. These values are called the upper and lower bounds. Lower bound can be a minimum required number of manufactured products and upper bound a maximum permissible quantity of a substance in the mixture. The thesis contain a formulation of original LP problems with lower and upper bounds which are solved by standard simplex method and by its modification for bounded variables. The aim of this study is to analyze and compare the reduced costs and shadow prices in the mentioned class of problems. At the end there will summarize the results of this work.


Optimization of production and distribution in bakery
Bilá, Tereza ; Kalčevová, Jana (advisor) ; Flusserová, Lenka (referee)
The subject of this bachelor thesis is optimization of production and distribution. The thesis aims to introduce the production problem in the case that the production limits are known and present its solution using a modified simplex method with lower or upper limits. The vehicle routing problem with one distribution centre and one vehicle will then be introduced. In the practical part of the thesis, these methods are applied in reallife data from the Martínek bakery business. The optimal production, which is targeting to maximize the profit under the given terms, and the optimal distribution from the bakery to shops, will be determined. At the end of the thesis, there is an evaluation of the given targets.

 

Fractal simplex algorithm in VBA
Ouzký, Karel ; Pelikán, Jan (advisor) ; Fábry, Jan (referee)
Basic idea of fractal simplex algorithm is based in the theory of matrix counting and knowledge of matrix representation of simplex tabuleao from revised simplex method. My desire is to explain theoretical basics on which this algorithm works and provide solution in language Visual Basic for Applications in application MS Excel 2007. Main benefit I see in the fact, that algorithm can solved specific class of mathematical problems in a way of exactness counting whithout necessity of using decimal numbers.
