Práce sumarizuje a dává do souvislostí vybrané úlohy operačního výzkumu, pro něž byly vyvinuty speciální optimalizační algoritmy či heuristiky kromě obecných algoritmů řešících problémy lineárního programování nebo diskrétního programování, s důrazem na praktické možnosti řešení těchto problémů danými algoritmy. Zabývá se běžnými úlohami lineárního programování s omezenými proměnnými, úlohami teorie grafů (toky, cesta grafem, kostra grafu), úlohou batohu, dopravním problémem, přiřazovacím problémem a úlohou obchodního cestujícího a srovnává speciální algoritmy s obecnými.

Title: Financial Mathematics in Czech textbooks from the Marchet's Reform Author: Martin Melcer Department: Department of Mathematics Education Supervisor: doc. RNDr. Martina Bečvářová, Ph.D. Abstract: The PhD thesis presents a comprehensive view of the development and the position of financial mathematics in Czech textbooks and collections particularly those used in high schools with consideration of the political situation in our country. The analysed period from 1908, i.e. from the Marchet's Reform, to the present is divided into five principal stages. In each stage textbooks covering financial mathematics instruction in all types of secondary schools are chosen. This shows the level and extent of the presentation, the complexity of the given tasks and problems and the way in which they are integrated into the textbooks or the syllabus, more precisely. At first the basic general characteristics of the textbooks are presented followed by a detailed description of partial topics of study which are then analysed thoroughly and mutually compared. The conclusions of the PhD thesis reflect the current situation of financial mathematics instruction and offer ways leading to the improvement in the level of financial literacy of our citizens. Keywords: financial mathematics, principal, interest, debt, annuity,...

Title: Solution of inverse problem for a flow around an airfoil Author: Mgr. Jan Šimák Department: Department of Numerical Mathematics Supervisor: prof. RNDr. Miloslav Feistauer, DrSc., dr. h. c., Department of Numerical Mathematics Abstract: The method described in this thesis deals with a solution of an inverse problem for a flow around an airfoil. It can be used to design an airfoil shape according to a specified velocity or pressure distribution along the chord line. The method is based on searching for a fixed point of an operator, which combines an approximate inverse and direct operator. The approximate inverse operator, derived on the basis of the thin airfoil theory, assigns a corresponding shape to the specified distribution. The resulting shape is then constructed using the mean camber line and thickness function. The direct operator determines the pressure or velocity distribution on the airfoil surface. We can apply a fast, simplified model of potential flow solved using the Fredholm integral equation, or a slower but more accurate model of RANS equations with a k-omega turbulence model. The method is intended for a subsonic flow.

The thesis follows up the competitiveness and tools necessary to achieve and maintain the competitiveness of an organization. This topic is currently rather crucial daily reality in the current market, and virtually all organizations were placed in the endless process of efforts for the development and subsequent maintenance of competitive advantages in order to be able to withstand the onslaught of competing companies in a particular market segment, the ongoing changes in the external environment and produce much needed profit, ensuring their continued existence. The aim is to identify ongoing processes in the selected organization, proposing critical success factors and determining the associated priority indicators affecting the competitiveness of the organization. For processing the theoretical part, an analysis of secondary sources was used, consisting of tightly-related publications, technical articles and Internet resources. The practical part of the work was based on an analysis of primary sources, on the qualitative research on the organization Gunnex s. r. o. The original intention to focus attention on the ongoing processes and critical success factors in the selected organization has proved to be beneficial not only for the purposes of this study, but also the organization itself . In collaboration with its leadership, three points were suggested aiming to improve the current position of the organization in an ongoing competition.

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Companies from multiple branches use as one way to offer their products and services network of sales representatives. This thesis study mainly designing process of such network and process of planning day to day routes of sales representatives with focus on minimizing cost caused by their work. For designing such network set covering problem model and matching problem model were used. For planning sales representatives routes travelling salesman problem, multiple salesperson travelling salesman problem, vehicle routing problem, nearest neighbor heuristic and authors own solution were used. Usage of multicriterial decision making is briefly mentioned as tool for managing such network on examples of equipment selection. As demonstration on real case, data from Tata Global Beverages (Jemča) company were used.

The thesis describes the principles of dynamic programming and it's application to concrete problems. (The travelling salesman problem, the knapsack problem, the shortest path priblem,the set covering problem.)

This thesis is aimed on time frame distribution task. In the theoretical part is described the mathematical model of this task and introduced in detail two concrete heuristics: greedy look-ahead and AKRed. In the practical part of the thesis has been a real situation solved with using of sophisticated optimalization software and through own implemented heuristic. These two solution are then compared each other and applicability of each heuristics for the given real problem is evaluated.

Increasing waste production is the reason why it is important to focus in more detail on profitable and cost side of waste economy. This diploma thesis deals with the area of garbage collection as a fundamental part during garbage their cumulation in a particular location and follow-up liquidation or preservation. At first the theoretical background of Chinese Postman Problem is described as a cornerstone for garbage collection models. Extensions of this problem have to be considered to be closer to reality. Then waste management in the city of Poděbrady is thoroughly described. In the final part of diploma thesis aforementioned theoretical models are applied on real data obtained from the city of Poděbrady waste department. Heuristic algorithms are an essential part of thesis as a replacement of optimizations models that cannot be used in some cases due to high requirements on computational time.

The diploma thesis focuses on tracing in layout by handlers between assembly lines in new plant for corporation Continental Automotive Czech Republic ltd, where boosters are produced. The theoretical part involves definitions of logistics, supply chain, material flow and handling equipment. Furthermore, methods of mathematic programming and software equipment are described, such as quadratic assignment problem, knapsack problem, travelling salesman problem from graph theory. In the practical part the situation in corporation has been analyzed and the data prepared for further examination. Then layout of plant and internal processes are evaluated and an appropriate model or concept of solution is selected. Subsequently, application in MS Excel is created with support of VBA scripts (3 kinds of layouts). The user manipulates with application followed by Solver for implementation of a new solution into practice. Finally, the models are interpreted and verified by Lingo. The focus of the thesis is the design of a layout change of a new plant including the description of tracing.