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Assignment problem with application to heath service
Tlapák, Martin ; Kopa, Miloš (advisor) ; Lachout, Petr (referee)
This bachelor's thesis deals with the theory of the nurse scheduling problem using the theory of integer programming. That is why we define basic concepts and present basic theorem of integer programming. We present the algorithm made for solving integer programming. Next we define a basic concept of as- sigment problem. We show how to solve assigment problem by the Hungarian method. Finally we solve the real nurse scheduling problem. The nurse's pref- erences are included in our model. We are finding solution which is suitable for the labour code of the Czech Republic and the special requests of the stressful workplace. 1
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Network flows and their modifications
Bitara, Matúš ; Hošek, Jaromír (referee) ; Popela, Pavel (advisor)
The thesis deals with optimization models in transportation problems. Brief introduction to graph theory and linear programming is followed by transportation problem of waste transport. Then there is a part with real data applied to the territory of the Czech Republic. After that the user interface created in Visual Basic programming language is explained. In conclusion computational results are discussed as well as their possible improvement.
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Engineering Process Optimization
Pluskal, Jaroslav ; Hrabec, Dušan (referee) ; Popela, Pavel (advisor)
This bachelor's thesis deals with optimization with emphasis on Newsvendor model and its usage. An overview of basic terms and theory related to probability, mathematical analysis and optimization is mentioned at the beginning. The main aim of this thesis is to formulate a Newsvendor problem in its basic form and then demonstrate the impact of various demand distributions. After that the gained knowledge is used to solve a project of factory, for which we want to set optimal parameters. Software GAMS is used to model and solve the project.
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Solving mixed-integer linear programming problems in GAMS
Škoda, Štěpán ; Branda, Martin (advisor) ; Kopa, Miloš (referee)
In the present work we study the problems of integer linear optimi- zation, at first from the theoretical point of view (Part I) and subsequently on the basis of empirical data (Part II). First section explains with what this field deals with and where is applied. Other sections contain annotated mathematical formulation of problems, definitions and theorems needed to understand the general methods for solving integer linear programs. In the last section of Part I, we introduce the two best known groups of algorithms that are used by commercial software. The second part provides more details on an Internet library that contains some practical problems, that has been needed to be solved in the past. Furthermore, there are sections dealing with solvers and the advanced options of GAMS. The last section presents data obtained in the course of solving problems using several codes (solvers) of software. 1
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Integer Optimization for Transportation Problems
Cabalka, Matouš ; Žák, Libor (referee) ; Popela, Pavel (advisor)
The thesis deals with optimization models in transportation problems with emphasis on traveling salesman problem. Brief introduction to the history is followed by theoretical part describing linear programming, integer programming and formulation of traveling salesman problem. Description of data preprocessing is included. Finally computational results are discussed and evaluated.
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Transformations of optimization models with aplications
Rychtář, Adam ; Bednář, Josef (referee) ; Popela, Pavel (advisor)
The thesis deals with recent problems of waste management in the Czech Republic. In connection with the existing software implementation, the author focuses on the gradual development of advanced mathematical programming models, which generalize existing approaches. The author applies acquired knowledge in the areas of network flows, linear, integer, and stochastic programming. The important role is played by modifications and transformations of the discussed models. They are further used to obtain the experimental results for real-world input data by implementation in GAMS.
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Optimization in Logistics
Huclová, Alena ; Škapa, Stanislav (referee) ; Popela, Pavel (advisor)
The thesis is focused on the optimization of models of transportation and transshipment problem with random demand, additional edges, and dynamic pricing. The theoretical part of the thesis introduces mathematical models of transportation. The software GAMS, which is used for the solution, is all so described. The practical part is a split among chapters and implements the described models by using real data.
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Optimization Models for Strategical Decision Making
Ulverová, Michaela ; Škapa, Stanislav (referee) ; Popela, Pavel (advisor)
The thesis deals with possibilities of mathematical modeling for public university budgets. Firstly, external conditions of public university financial inflows are discussed and~illustrated by using particular data. The related basic legislature is introduced. In~the~next part, internal financial flows are described the help of a general scheme. Step-by-step, a mathematical model of the university budget was built with using analysis of existing data, rules and formulas. The proposed model represents nonlinear multi–stage scenario-based stochastic programme, involving linear and network-flow like constraints. It allows to take into account more objective functions and related parametric analysis. The model was implemented in the algebraic modeling system GAMS with~interface to MS Excel. The aim of the presented mathematical model was not to offer a tool that would be used for automatic distribution of financial resources of the university, but to give flexible possibilities to its user to realize computational experiments and in this way to achieve a deeper insight into the modeled problem.
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A Comparison of Optimization Programmes
Kovářík, Dušan ; Dvořák, Jiří (referee) ; Šeda, Miloš (advisor)
The thesis is focused on various free available software, designed for mathematical optimization. In the first section, the current offerings on the optimization software market are introduced. Further on, the thesis is dealing in details with selected pieces of software products – specifically GAMS, LINGO, QMS web service (Quantitative Methods Software) and Investigator tool, embedded in MS Office Excel application. The closing part, then, is concerned with testing and comparison of above presented software products, employing the performance tests with pre-selected optimization tasks.
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Optimization Modelling Languages
Molliková, Eva ; Škapa, Stanislav (referee) ; Popela, Pavel (advisor)
The goal of the thesis is to introduce readers into the use of the GAMS modelling language that is an important tool for optimization model building. The overview of useful mathematical concepts introduces the text. The main part of thesis contains four examples presented in detail. Firstly, the basic GAMS related concepts, statements and techniques involving analysis of results are described. The second example illustrates development of model description beginning from quite specific instance towards general and flexible one. Two examples solved at the end show further use of the GAMS and can motivate reader to enhance their konwledge and apply optimization in his areas of specialization.
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