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Sudoku - formulation and solving the problem
Jelínek, Tomáš ; Jablonský, Josef (advisor) ; Chrobok, Viktor (referee)
This bachelor thesis deal with the Sudoku game, there are delevoped models for solving the Sudoku and model for problem generation. There are described the rules of the game, history and some possible modifications in the first chapters. Models are developed in environment Xpress-IVE, there are described some of its features. Models for solving the Sudoku are being used two approaches - linear programming and constraint programming. Both methods are described, there are made mathematical models, which are then re-written in Mosel language. There are used both methods in model for problem generation, algorithm works on principle, where numbers are gradually removed from full Sudoku table.
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Analysis of the cereal food products using mathematical modelling
Grygárková, Eva ; Jablonský, Josef (advisor) ; Škulavíková, Štěpánka (referee)
The bachelor thesis deals with nutritional values of cereal food products from three companies (Nestlé, Bona Vita and Emco). In the first part of the thesis linear programming models are described. The next chapter deals with the characteristics of the real situation in which Guideline Daily Amounts and nutritional values of specific cereal food products are set, and economic and mathematical model is formulated. The last part is devoted to numerical experiments. At first, the models are solved in MS Excel 2007 and then some of them are analysed in LINGO modelling system. The main aim of the thesis is to determine whether cereal food products are healthy and nutritious in terms of their nutritional values. The proposed models determine the individual portions of cereal food products consumed per day using the minimum costs that are spent for the purchase of the products.
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Usage of graph theory in distribution problem
Libichová, Tereza ; Kuncová, Martina (advisor) ; Skočdopolová, Veronika (referee)
The purpose of this thesis is to acquaint a reader with basic history, definitions and methods of a graph theory and also to show a practical usage of those methods. In the first theoretic part there are explained basic concepts of graph theory with additional graph illustrations. Further there are explanations of basic exercises types, such as exercises of optimal cycles, minimal spanning tree and optimal ways. In the second parts there are briefly introduced optimalization systems and with all the details is described a Lingo programme, in which the practical part will be processed. In those practical parts we will apply already clarified optimalization exercises on a real example.
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Optimization over the internet
Šálek, Pavel ; Jablonský, Josef (advisor) ; Rada, Miroslav (referee)
The goal of this thesis is to analyse and evaluate the efficiency of systems used for solving problems of mathematical programming, which are available within the frame of project NEOS (Network Enabled Optimization Server). The most frequent algorithms for solving linear programming and mixed integer programming are described in the beginning of the work -- simplex algorithms, the interior point method, cutting plane method and branch and bound method. These algorithms are used in solvers, which are supported by NEOS server. The efficiency of the algorithms and solvers are tested on collection of chosen problems contained in libraries of NETLIB and MIPLIB.
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Application of Linear Programming on Project Management
Hrnčířová, Michala ; Zouhar, Jan (advisor) ; Fábry, Jan (referee)
There are two approaches to solving project management tasks. The first method is using specialized algorithms that do not always give optimal results. The second way is to use linear programming which includes designing mathematical models that are then solved by optimization systems. In my thesis I am dealing with three types of optimization tasks, two of which are basic linear programming tasks: basic project time scheduling and time scheduling of a project with variable action lengths. The focal point of the thesis is to assemble a mathematical model to solve the time scheduling of a project with limited resources. My goal is to design general mathematical models and to compare the results gained by the use of linear programming with those of specialized algorithms.
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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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Using of AIMMS at solving of optimization models
Lacinová, Věra ; Jablonský, Josef (advisor) ; Zouhar, Jan (referee)
The bachelor's thesis is about AIMMS -- a system for mathematical modeling. The aim of the thesis is to create a simple user's guide for interested individuals that want to use this system on the basic level. Practical part is about making models of selected distribution problems. Thesis is organized into three main chapters. The first chapter is about linear programming and selected distribution problems of linear programming. There is outlined development of linear programming and its place in mathematical modeling. In this chapter, mathematical models of selected distribution problems as transportation problem, container-transportation problem, allocation problem, covering problem and assignment problem are formulated. The second chapter is about AIMMS and describes how to work with this system. It contains basic information about the system and its author J. Bisschop. The next part informs how to work with system AIMMS. There is a way of declaration of individual sections and procedures in Model Explorer discussed. The AIMMS Page Manager, a tool for creating end-user's pages, is described. By this tool the end-user can change data sets and obtain results of analyzed problems. The third chapter is practical part. It contains the description of selected distribution problems with the emphasis on their implementation in AIMMS. Appendix contains end-pages of selected distribution problems and the list of solvers supported by AIMMS.
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Optimization of ideal nutriment
Šádová, Eva ; Kuncová, Martina (advisor) ; Šindelářová, Irena (referee)
The thesis describes a way of searching the best bill of fare for certain patient in hospital. The target is to set up and then to solve an optimization model. Criterion of performance is to minimize spending on selected foodstuff. The first part describes a theory of optimization models, the second is about nutrition and the third aims to solve a model and to interpret the results.
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Practical application of cutting problem with atypical targets
Marcineková, Petra ; Kalčevová, Jana (advisor) ; Šmídová, Milada (referee)
This bachelor work deals with one of the linear programming problems, the problem of optimal dividing of the material. The typical targets of these problems in classes is to minimize waste and minimize the material used. The aim of this work is the formulation of the unusual targets of this problem. These atypical targets include minimizing the number of cuts, counting waste nicked by cutting-off or to ensure a certain proportion of final products. Part of this work is the practical application of those unusual modifications of cutting problem.
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