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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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Advanced optimisation model for circular economy
Pluskal, Jaroslav ; Bednář, Josef (referee) ; Šomplák, Radovan (advisor)
This diploma thesis deals with application optimization method in circular economy branch. The introduction is focused on explaining main features of the issue and its benefits for economy and environment. Afterwards are mentioned some obstacles, which are preventing transition from current waste management. Mathematical apparatus, which is used in practical section, is described in the thesis. Core of the thesis is mathematical optimization model, which is implemented in the GAMS software, and generator of input data is made in VBA. The model includes all of significant waste management options with respect to economic and enviromental aspect, including transport. Functionality is then demostrated on a small task. Key thesis result is application of the model on real data concerning Czech Republic. In conclusion an analysis of computation difficulty, given the scale of the task, is accomplished.
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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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Modelling of Selected Risks in Healthcare
Nováková, Pavlína ; Bednář, Josef (referee) ; Popela, Pavel (advisor)
The diploma thesis deals with the modeling of selected risks in healthcare. Motivated by the current pandemic situation, it focuses on analysis of risks associated with the vaccination center in Brno. The theoretical part is mainly devoted to the issue of risk management with a focus on risks in healthcare, where the methods that are used in the practical part are defined. Furthermore, the thesis presents selected topics of mathematical programming. Especially, the newsvendor problem is introduced as inspiring case for further modelling. The brief description of the covid-19 pandemic situation later serves as one of the data sources. The practical part deals with the description and risk analysis of the vaccination process using the methods "What If?" and the FMEA method. Appropriate decisions are then proposed for selected risk situations using the GAMS optimization system. Based on the results of the calculations, specific recommendations are proposed.
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Budget Optimization
Golasowski, Martin ; Janíček, Ladislav (referee) ; Popela, Pavel (advisor)
The bachelor's thesis aims to approach the issue of creating a budget for a public university and the subsequent creation of a mathematical model. The thesis explains the rules and formulas for the distribution of funds for higher education to individual universities. Then, the formulas for the redistribution of these funds between individual faculties are given. Subsequently, a mathematical model of nonlinear programming in the GAMS system is built using real data and constraints. The model is then used to examine the change in the distribution of funds for various objective functions. The aim of compiling the model was not to offer a tool that will be automatically used for the distribution of funds at BUT, but to provide its users with a wider range of computational experiments and gain better insight into the problem.
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Optimization models in population protection
Mihálová, Veronika ; Cabalka, Matouš (referee) ; Popela, Pavel (advisor)
This master thesis utilizes operational research principles to model and address emergency events, with a focus on rapidly and effectively making decisions related to population sheltering and the allocation of security forces during such crises. The theoretical section provides fundamental information about the current state and application of risk management in civil security while defining terms directly associated with population protection and crisis management. Moreover, it explores the historical application of mathematical programming and optimization in crisis management processes. In the practical segment of the thesis, the fundamental traffic problem is adapted to address the issue of establishing permanent civil protection shelters in the Brno-Židenice district. The models are solved using the GAMS program, building upon a comprehensive risk analysis that meticulously identifies key components of the population protection system. Furthermore, potential risk scenarios for the system are formulated using the FMEA method. The results obtained, which outline optimal allocation strategies for residents and security forces, are visually presented on maps. Recommendations are provided for future planning and crisis management in emergency events.
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Advanced Stochastic Programming Models in Power Engineering
Pavelka, Ondřej ; Štětina, Josef (referee) ; Popela, Pavel (advisor)
This diploma thesis applies stochastic optimization in the field of the power engineering. In the thesis first part, the needed mathematical theory is described, specifically mathematical, linear, nonlinear, integer and stochastic programming. The second part deals with the heating plant, in which heat is generated by gas and biomass boilers. The aim of this thesis is to design a model for the schedule planning of these boilers. The model is based on two stage stochastic programming with scenario approach. Then the model is solved by GAMS software. In the final part of the text, the focus is on the model sensitivity analysis and suggestions for future improvement.
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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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Optimization Risk Modelling in GAMS
Kutílek, Vladislav ; Bednář, Josef (referee) ; Popela, Pavel (advisor)
The diploma thesis deals with the possibilities of using the optimization modelling software system GAMS in risk management. According to the assignment, emphasis is placed on a detailed approach to the program for those, who are interested in its use in the field of risk engineering applications. The first part of the thesis contains the knowledge to understand what the GAMS program is and what it is used for. The next part of the work provides instructions on how to download, install, activate the program and what the user interface of the program looks like. Thanks to mathematical programming, it will be explained on a project on the distribution of lung ventilators, what basic approaches may be used in risk modelling in the GAMS program on a deterministic model. The following are more complex wait-and-see models, which contains the probability parameters and here-and-now models, where we work with demand scenarios and verify whether if they meets the requirements of other scenarios or calculate costs for the highest demands. The two-stage model is also one of the here-and-now models, but it is significantly more complex in its size and range of input data, it includes additional price parameters for added or removed pieces of lung ventilators from the order.
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