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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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Mathematical Optimisation of Geometry of the Microstructured Bipolar Electrolyser
Kodým, R. ; Bystroň, T. ; Křišťál, Jiří ; Jiřičný, Vladimír ; Bouzek, K.
In this work a 3-dimmensional mathematical model of the secondary current density distribution has been proposed and implemented. A parametric study of the influence of selected geometrical parameters, electrolyte conductivity and current load on the parasitic current value was performed. The Laplace equation describing the Galvani potential distribution was solved by Finite Element Method in COMSOL Multiphysics^TM environment. The mathematical model results have shown that the value of parasitic current is mainly affected by the electrolyte conductivity and interelectrode distance (i.e. active cross-section of the electrolyte distributors). Using the geometry optimization the parasitic currents have been minimized to an acceptable value, i.e. below the 5% of the total current load.
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Matematické modely hydraulických systémů, příklady, analýza
Straškraba, Ivan
The purpose of this contribution is to describe some phenomena arising in hydraulic systems. By a hydraulic system we call a network of tubes, pumps, valves, accumulators and other elements designed to fulfil certain function, for example pumping water from one tank to another. To quantify the fluid flow through the system in question we use fundamental physical principles, namely conservation of mass, momentum and energy. In pipes it leads to Navier-Stokes equations simplified with regard to the special properties of the flow. For description of the fluid flow through other hydraulic elements different models are used which must be identified by the help of experiments performed on an appropriately designed test ring.
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Some possibilities of analytical description of strong non-adiabatic gas compression
Bayer, Zdeněk
Paper deals with modelling of the gas state- and thermodynamic behaviour in cavitation bubbles. After recent presentation of model M3 based on the more realistic idea of the heat transfer in the course of bubble compression, introduces its advanced version M4. The comparison of the polytropic and M4 model of process shows the results for high volume compression ratios may differ in tenths of percent. In a like range lies the discrepancy caused by using more accurate state equation and temperature dependence of the heat capacity.
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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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