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Discrete versions of continuous financial models
Graeber, Jiří ; Hurt, Jan (advisor) ; Zahradník, Petr (referee)
This thesis studies the continuous-time financial models and their discrete versions, used for simulations and parameters estimations. Firstly, various stock price development and interest rates models are introduced. As a result of their uncertain future dynamics, these are defined as continuous-time stochastic processes. Secondly, a summary of discrete versions of continuous-time models, formed by Euler and Milstein discretization schemes, i.e. two most frequent ways of approximating a time-continuous stochastic process, is looked at. According to these discrete versions, simulations with different parameters are conducted in the third part of the thesis in order to illustrate individual behaviour of these models. In the conclusion, a comparison of a unique trajectory specified by the real data of one year interest rates swaps and of the simulations of Vasicek and Cox-Ingersoll-Ross model with parameters estimated from the real data is shown.
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Discrete versions of continuous financial models
Graeber, Jiří ; Hurt, Jan (advisor) ; Zahradník, Petr (referee)
This thesis studies the continuous-time financial models and their discrete versions, used for simulations and parameters estimations. Firstly, various stock price development and interest rates models are introduced. As a result of their uncertain future dynamics, these are defined as continuous-time stochastic processes. Secondly, a summary of discrete versions of continuous-time models, formed by Euler and Milstein discretization schemes, i.e. two most frequent ways of approximating a time-continuous stochastic process, is looked at. According to these discrete versions, simulations with different parameters are conducted in the third part of the thesis in order to illustrate individual behaviour of these models. In the conclusion, a comparison of a unique trajectory specified by the real data of one year interest rates swaps and of the simulations of Vasicek and Cox-Ingersoll-Ross model with parameters estimated from the real data is shown.
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Optimizing Parcel’s Delivery of Czech Post
Svojšová, Kateřina ; Skočdopolová, Veronika (advisor) ; Borovička, Adam (referee)
The aim of my bachelor's thesis is to optimize the parcel's delivery of the Czech post in the surroundings of Kolín and Kutná Hora, which is operated by Depo Kolín 70. This service's speciality is that the parcels are being delivered to individual post offices according to the zip code. The main task is to minimize costs of delivery on these parcels, the next thing is to settle the optimal count of cycles assuming that delivery car has to come back to the Depo and another thing is to consider an opening time of post offices. Discrete models are used to solve this problem, specifically vehicle routing problem with time windows. To solve this model has been used LINGO optimizing software.
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Multiple criteria evaluation of alternatives support systems and their comparison
Kvasničková, Marie ; Sekničková, Jana (advisor) ; Kuncová, Martina (referee)
Multiple criteria decision making can be divided into two categories, concretely to multiple criteria evaluation of alternatives and multiple criteria programming. This bachelor thesis deals with the easier one -- multiple criteria evaluation of alternatives. Analysis of these problems is in general made with the use of software support, which is vital in these days. Range of this software is wide, whether it's MS Excel application, individual program or web-based application. Aim of submitted thesis is to try out this software. It also deals with brief description of these systems together with their comparison.
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Recreational mathematics problem solving as an integer programing problems
Künzelová, Barbora ; Jablonský, Josef (advisor) ; Rada, Miroslav (referee)
The bachelor thesis deals with the solution of three selected recreational mathematics problems using discrete optimization. These problems are called Gridspeed Puzzle, Shifty Witnesses and Alien Tiles. The reader first learns the rules of these games of which are then formulated mathematical models that are integer in all cases. The first two games have one model and are being solved one way, but in game Alien Tiles are solved several optimization problems. All models are rewritten MPL modeling language in which they are solved by solver CPLEX. For all selected problems are found optimal integer solution, which is then described and explained to the reader. The solution results of the task Alien Tiles are finally compared and we are able to tell that one form of the desired outcome of the game is more difficult to calculate.
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Application of Heuristics on Vehicle Routing Problem
Gerlich, Michal ; Fábry, Jan (advisor) ; Pelikán, Jan (referee)
This thesis deals with solving a real case from one specific part of Operations Research -- Discrete Models. The case can be classified as Vehicle Routing Problem (VRP) which is a subset of classical Travelling Salesman Problem (TSP). The VRP is modified TSP when requirements of customers and capacities of trucks play role. The data needed for calculations were taken from the real situation of Pivovar Svijany a.s. The problem can be defined as VRP with cars with different capacities and split delivery. Even though the mathematic model of the problem is known and described in the thesis, the size of the problem is too big to be optimized. Therefore heuristic was used to solve it. Because of the good computational results in the past the savings algorithm was chosen. Its model was set using Visual Basic for Applications (VBA). The thesis (among others) analyses the sensitivity of the output on the values of the factors that can be chosen by the analyst. At the end of the thesis the best found solution is presented and the initial and the new scheme of the circles are compared.
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Analyses and optimization of efficiency in agriculture and wood-working company
Jágerová, Tereza ; Fábry, Jan (advisor) ; Pelikán, Jan (referee)
This thesis aspires to optimize the processes in agriculture and wood-working company and to propose some changes if needed. At first, it is wood-working branch which is analyzed. The intent is to find an optimal route to distribute pallets and afterwards freight the vehicle by sawn wood and return back with. This is some modification of travelling salesman problem with more than one salesman and more centers including the condition that the travelling is dynamic in time and that only selected clients are visited. The agriculture problem is more complicated and complex because the model aims to find an optimal portfolio of diverse animal and vegetal production influenced by many factors and some of them are mentioned below. The agriculture model includes for example the stochastic character of weather and the condition that the herd of cattle should be stable.
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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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