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Optimization of the TV ad planning using mathematical models
Petruška, Tomáš ; Jablonský, Josef (advisor) ; Kalčevová, Jana (referee)
Planning and optimization of TV advertising space in the area of the Czech media market requires a knowledge of features of the problem and systems that are able to suggest the best results from data taken from measurement of TV audience, which is complex and demands special capacity. These results should be obtained (calculated) by using mathematical optimization models. Results depend on the objectives of company. The content of this thesis is to create and implement mathematical models, which serve to solve practical problems about planning advertising space and commercial blocks. The work deals with the characteristics of the television media market, audience measurement, the factors that influence the ratings, as well as an examination of other indicators that are necessary for the planning and optimization of TV advertising. Besides familiarizing the reader with the operations of buying advertising space, this paper`s goal is to demonstrate newly created mathematical models that are applicable to the work of TV channels, media agencies or other companies, which deal with the optimization of the television media market.
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Solving the Battleship Solitaire puzzle as an integer programming problem
Přibylová, Lenka ; Jablonský, Josef (advisor) ; Fábry, Jan (referee)
The bachelor thesis deals with the Battleship Solitaire puzzle. It introduces the history and the rules of this puzzle, which are thereafter used to formulate the puzzle as an integer programming problem. Two mathematical models based on different approaches are created, a cell-based model and a ship-based model. In order to determine whether a puzzle has a unique solution an objective function is added to each model. Both models are developed in LINGO modeling language and tested with different grid sizes. The test results show that even though the ship-based model uses fewer variables and constraints, it is too demanding in terms of data processing. It results in longer solving times and the model fails to find a solution for larger grids. Solving the problem using the cell-based model is significantly faster. The solution was found even for larger grids, though the solving time was very long.
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Efficiency evaluation models and their applications
MARKOVÁ, Klára
Thesis themed "Efficiency evaluation models and their applications" deals with mathematical models for the efficiency evaluation of comparable production units and targets the utilization of Data Envelopment Analysis (DEA) for this purpose. The thesis aims first to describe DEA models and mention possibilities of their application and then to practise the theoretical knowledge by using proper software in a factual instance. To reach this aim the thesis is composed of two parts {--} theoretical abstract and practical application. The abstract contains basic theory of DEA: fundamental principles, input data and results and description of primary, alternate and modified models. A summary of software applications that can evaluate efficiency using DEA follows. The abstract is closed with some real examples of DEA applications in practice. The second part of the thesis arose from cooperation with a fire department of a factual region of the Czech Republic. The efficiency of its 16 fire stations is compared by using a proper DEA model. A number of actions (output) and a number of employees, a level of fire equipment and an inside area (inputs) are established for each fire station on the strength of the fire department{\crq}s statistics, databases and estimations. The efficiency calculation is performed through the use of the Frontier Analyst Professional, software application specially made for the DEA analysis. Regarding the outputs uncontrollable character an input-oriented DEA model is chosen for the calculation of the fire stations efficiency. A result of the DEA efficiency analysis consists in separating the effective and ineffective fire stations of the surveyed fire department. The potential improvement (inputs decrease), necessary to reach the maximal efficiency, is proposed to each ineffective fire station. This suggestion is further adapted with respect to the real feasibility and the Czech legislative order. The practical part of the thesis is concluded with appreciation to what degree the stated targets were reached and to what degree the application of the DEA method to comparing the factual fire stations efficiency was rewarding.
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Investing in the Czech Republic in Relation to HDP
Jiráková, Eliška ; Bartošová, Jitka (advisor) ; Votava, Libor (referee)
Investment has undergone dramatic development lately and people are looking more and more new ways to evaluate their funds to protect them from the effects of inflation or as easy to get rich This work deals with investment opportunities for Czechs in relation to their income and appreciation in relation to the welfare of the country measured by GDP. The first part describes the history of investment and investment opportunities. Subsequently, the work deals with the development of GDP and of the allocation of funds in various investment instruments in the development of GDP. The last part is devoted to modeling the development of further investment on GDP in the CR.
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Hybrid flowshop with adjustment
Kaněra, Vojtěch ; Pelikán, Jan (advisor)
This work should serve as a source of information on the issue of production scheduling. The work is particularly focused on the relatively new terms in optimization of processing of production batches area, such as flowshop and its modifications in the form of so-called hybrid flowshop. The work is divided into five chapters. The first chapter consists of an introduction. In the second chapter I mention the theory of scheduling, the third part deals with the history of flowshop and in the fourth part I check the functionality of new models on real data. In conclusion I summarize the contents of work, comment resulting calculations and deliver the practical usage of flowshop.
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Mathematical optimization of schedule at high school
Daněk, Roman ; Fábry, Jan (advisor) ; Jablonský, Josef (referee)
Tato diplomová práce zabývající se matematickou optimalizací rozvrhu na střední škole si klade za cíl prošetřit, zda je vhodné k optimalizaci středoškolského rozvrhu použít dělící problém. Veškeré výpočty jsou dokumentovány ve třech různých úlohách, které se zakládají na reálných datech skutečné střední školy. Z optimalizačních softwarů byly zvoleny programy Lingo a Xpress na kterých byly ověřeny dva rozdílné způsoby formulace matematického modelu. Práce obsahuje sedm příloh, které jsou obsaženy v hlavním dokumentu a speciální přílohy obsahující formulace modelů a interpretační tabulky v programu MS Excel s využitím VBA na přiloženém CD.
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