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Optimal Scheduling Systems for Outdoor Activity
Rykala, Kryštof ; Matyáš, Jiří (referee) ; Češka, Milan (advisor)
The thesis discusses technologies and approaches for implementation of information system. Its part and motivation is automatic scheduling of activities. A model for resource-contraint project scheduling is defined using mixed-integer linear programming. Part of this thesis are client, server and planning programs that form a system for management of an outdoor center with automatic scheduling of activities.
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Modelling of the waste flow in the Czech Republic
Němcová, Lucie ; Procházka, Vít (referee) ; Šomplák, Radovan (advisor)
Strategic planning is the basis for efficient and sustainable waste management. Data collection and its deep understanding are essential for effective planning. Waste flows are an important information to assess waste management to date. This information has so far been available only aggregated at national level in the Czech Republic. In this thesis, an approach has been developed to reconstruct the waste flows at a sub-national level from available data. The approach consists of two optimization models: partial and final. The partial model is based on expert assumptions. The reconstruction of the flows by the partial model is done sequentially in smaller groups of flows. The computation of the partial model is repeated with different composition of the groups of flows optimized at the same time. Each iteration results in a~candidate solution which is used as an input data for the final model. The solution of the final model yields the final reconstruction of the waste flows. Model development and testing was carried out on problems simulated based on the real data from the waste management of the Czech Republic.
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Optimal Scheduling Systems for Outdoor Activity
Rykala, Kryštof ; Matyáš, Jiří (referee) ; Češka, Milan (advisor)
The thesis discusses technologies and approaches for implementation of information system. Its part and motivation is automatic scheduling of activities. A model for resource-contraint project scheduling is defined using mixed-integer linear programming. Part of this thesis are client, server and planning programs that form a system for management of an outdoor center with automatic scheduling of activities.
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Aplikace optimalizačních metod na problémy výroby elektřiny
Šumbera, Jiří ; Dlouhý, Martin (advisor) ; Pelikán, Jan (referee) ; Hančlová, Jana (referee)
This thesis deals with application of optimisation methods based on linear and mixed-integer linear programming to various problems in the power sector related to electricity production. The thesis goal is to test the applicability of such methods to formulating and solving various instances from the class of real-world electricity production problems, and to find the advantages and disadvantages associated with using these methods. Introductory chapters describe the main characteristics of power markets, including the historical and regulatory context. Fundamental properties of power markets on both demand and supply side are also described, both from a real-world and a modelling point of view. Benefits of optimisation and modelling are discussed, in particular the solution feasibility and optimality as well as insights gained from sensitivity analysis which is often difficult to replicate with the original system. In the core of the thesis, optimisation techniques are applied to three case studies, each of which deals with a specific problem arising during electricity production. In the first problem, the profit of gas-fired power plant in Slovakia from selling power on the day-ahead market is maximised. The model is set up using both technical and commercial constraints. The second problem deals with the problem of representing a two-dimensional production function which primarily arises for a hydro generator with large variations in the level of its reservoir. Several representations of the original function using piecewise linear subsets are presented, compared, and characterised by their computational intensity both theoretically and practically. In the third problem, the prices on the German day-ahead market in 2011 are modelled. Contrary to the previous two models, the model does not capture an optimisation problem faced by a single producer, but incorporates a large subset of the whole market instead. Consequently the model is formed out of generic constraints relevant to all power plants whose parameters are estimated. By combining information about the aggregate availability of power plants with the estimated efficiencies a full supply curve for each day is created. Different scenarios are analysed to test the impact of uncertain inputs such as unknown or estimated constraints. The choice of the investigated problems stems from the attempt to cover electricity production problems from the point of view of multiple criteria. The three investigated electricity production problems span a broad range from the decisions of a single power plant to the modelling a power market as a whole. Formulations of the production function with different level of detail are presented ranging from a simple linear relationship to several bivariate function formulations. While each problem answers a specific question, they all illustrate the ease with which various electricity production problems can solved using optimisation methods based on linear and mixed-integer linear programming. This is mainly due to the ability of these methods to approximate even non-linear functions and constraints over non-convex domains and find global solutions in reasonable time. Moreover, models formulated with these methods allow sensitivity and scenario analyses to be carried out easily as is illustrated in each of the case studies.
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Selected methods for solving integer programming problems
Picková, Veronika ; Sekničková, Jana (advisor) ; Charvát, Karel (referee)
This final thesis work is dealing with the problems of mixed integer linear programming and their possible methods of solving. The reader will be introduced to the issues of integer programming in the first part of the work. There follow the different methods of solving in the second part, concretely the possibility of solving without the integer constraints and rounding the solution, the branch and bound method and the Gomory's method. The purpose of this work is to inform the reader about the Benders decomposing algorithm. Decomposing methods divide the original problem into two parts: a part with the constraints of integrity and a part without them. All of the explained methods are supported by illustrative examples. The third part of this thesis is the application of used methods to a concrete problem.
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Comparison of professional optimization systems performance
Rýdlová, Lenka ; Jablonský, Josef (advisor) ; Charvát, Karel (referee)
The problems of linear programming are very extensive in practice and professional optimization systems are necessary to their solution. Most of the time, these problems concern mixed integer programming. These types of problems have to be solved other then simplex method, even if the other methods are based on it. Integer conditions cause high difficulty with solving and disproportionately prolong solution time. These problems can be found in an electronically library MIPLIB. The library is used to testing optimization systems, which are whole range. The best programs on the market are CPLEX, Gurobi, Xpress and LINGO, used at our university. The focus of this thesis is testing the performance of each program listed above. The comparison is done based on solution time and accuracy of the calculated optimal solution.
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Application of optimization methods in e-shopping
Hollayová, Nela ; Zouhar, Jan (advisor) ; Fábry, Jan (referee)
The subject of the thesis is the optimization of one the key processes in a book e-shop, namely delivery of goods from suppliers. In particular, we focus on the problems of selection of suppliers and the subsequent route optimization in daily pick-ups of orders. The proposed solution uses a combination of two mixed integer programming models. The model for supplier selection was designed so as to reflect the empiric approaches that are currently employed in the e-shop; the model for route optimization is a modified version of the canonical travelling salesman problem. On the basis of achieved results, we presented effective procedures for solving both of the aforementioned problems and suggested their implementation into the e-shop's enterprise resource planning system.
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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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