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Design and application of heuristics in distribution of ordered products to the consumers of NIKOL NÁPOJE a. s. company
Solnická, Veronika ; Fábry, Jan (advisor) ; Pelikán, Jan (referee)
This thesis deals with the optimization of distribution of products to consumers based on a real case study of a particular company from Opava. For this purpose, a mathematical optimization model is used to illustrate the vehicle routing problem. The study will also offer an explanation on the relevancy of heuristic methods, mainly with respect to their application in solving real life situations analogous to the one surveyed. On the basis of chosen heuristic methods (i.e. the nearest neighbour algorithm and the savings algorithm) and having taken into account the restricting conditions of the company, four algorithms were designed. These four algorithms are programmed in Visual Basic for Applications MS Excel 2007. They are aimed at solving the real problems with the distribution of ordered products that the particular company must deal with. The thesis compares the results provided by an employee of this company, and the results presented by the designed algorithms.
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Methods for construction of zero-coupon yield curve from the Czech coupon bond market
Hladíková, Hana ; Radová, Jarmila (advisor) ; Pelikán, Jan (referee) ; Onder, Štěpán (referee)
The zero coupon yield curve is one of the most fundamental tools in finance and is essential in the pricing of various fixed-income securities. Zero coupon rates are not observable in the market for a range of maturities. Therefore, an estimation methodology is required to derive the zero coupon yield curves from observable data. If we deal with approximations of empirical data to create yield curves it is necessary to choose suitable mathematical functions. We discuss the following methods: the methods based on cubic spline functions, methods employing linear combination of the Fourier or exponential basis functions and the parametric model of Nelson and Siegel. The current mathematical apparatus employed for this kind of approximation is outlined. In order to find parameters of the models we employ the least squares minimization of computed and observed prices. The theoretical background is applied to an estimation of the zero-coupon yield curves derived from the Czech coupon bond market. Application of proper smoothing functions and weights of bonds is crucial if we want to select a method which performs best according to given criteria. The best performance is obtained for Bspline models with smoothing.
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Optimization distribution and collection of infusion solutions
Kravciv, Zbyněk ; Fábry, Jan (advisor) ; Pelikán, Jan (referee)
There are many distribution tasks, that vary in a number of vehicles, time windows, dividend or undivided delivery or if it is static problems or dynamic problems. In this essay I focus just on few of them. At first I put my mind to simple statistic distribution task with one vehicle. Later I extend it with time windows, when the point can be served by one car and by many cars. In the essay it will be solved the real task of distribution and delivery transportation of infusion in the hospitals. Because of the difficulty of solution I have to use the heuristic methods - Method of nearest neighbour, Savings method and Insert method. All these methods are modified by capacity requirements, time windows and also observence of the rules, which the drivers have to keep during a distribution. The aim is to minimize the distance travelled by the vehicles. And at least the company could be recommended the best solution.
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Scheduling in systems with multiple machines
Černý, Jan ; Pelikán, Jan (advisor) ; Zouhar, Jan (referee)
This paper focuses on characterization of scheduling in systems with one or multiple machines. There are different types of tasks given, with which we can encounter in scheduling. At the beginning, introduce basic concepts of production scheduling. The second chapter is a flowshop problem with its history and projections for the flowshop problem. In the next chapter is a modification of flowshop problem called hybrid flowshop, which is divided according flexibility to hybrid flowshop with processing flexibility and hybrid flowshop with routing flexibility. Another chapter is open shop problem, which have some differences compare with the above mentioned types. The last chapter is a job shop, stating in a graphical solution for two machines and a brief description of the algorithm Shifting bottleneck.
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Fractal simplex algorithm in VBA
Ouzký, Karel ; Pelikán, Jan (advisor) ; Fábry, Jan (referee)
Basic idea of fractal simplex algorithm is based in the theory of matrix counting and knowledge of matrix representation of simplex tabuleao from revised simplex method. My desire is to explain theoretical basics on which this algorithm works and provide solution in language Visual Basic for Applications in application MS Excel 2007. Main benefit I see in the fact, that algorithm can solved specific class of mathematical problems in a way of exactness counting whithout necessity of using decimal numbers.
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Optimization of road maintenance
Dojčar, Martin ; Fábry, Jan (advisor) ; Pelikán, Jan (referee)
While creating a state budget it is always important to reduce the expenditures in the public sector. Among other possibilities, this could be reached by finding the optimal routes of road maintenance vehicles. These vehicles take care about the road network while considering all the conditions and restrictions related to this task. Since the objective is limited by several restrictions as well as conditions, a number of procedures is required to handle them progressively. A very important role in this task is featured by the postman problem, which all the procedures used are derived from. And they are as following: the undirected chinese postman problem, the directed chinese postman problem, the hierarchical postman problem and finally the capacitated postman problem. All these problems are also generally described in this thesis, so that they can be reused for a calculation of similar tasks, such as street sweeping, garbage collection, mail delivering or defining of the optimal school bus routes.
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Stochastické modely a jejich řešení v MS Excel
Müller, Jan ; Kořenář, Václav (advisor) ; Pelikán, Jan (referee)
The aim of this thesis is to create an application in MS Excel, which would have been able to count on basic stock models, and Markov decision processes with alternatives. This issue is devoted to the first part of the work. This is the theory needed to understand the basic principles and method of calculation tasks. The second part describes the developed application that can be solved one-product and multiproduct deterministic stock models, stochastic stock models and Markov decision processes with alternatives, and changing valuation of the transition. The description is supplemented with graphic images directly from the application, which makes using applications easier to understand. The part of work is also CD with created application.
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Optimization of electronic goods distribution
Svobodová, Šárka ; Fábry, Jan (advisor) ; Pelikán, Jan (referee)
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.
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Rozvrhování výroby - teorie a praxe
Kašpar, Michal ; Pelikán, Jan (advisor) ; Kuncová, Martina (referee)
Manufactural activity is the basis of every sound economy. The risk for today's industrial establishments in our let us say european conditions is to hold competitiveness in the terms of global economy. This diploma thesis is focusing on solving problems of manufacturing scheduling with the view of theory and practice. It is impeach of real-life production. Scheduling belongs to hard combinatorial problems and therefore are usually solved by various heuristic or metaheuristic methods. For application of mentioned metaheuristic methods is important to use suitable choice of representative data.
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Dynamic models of the demand for money. Application to the Czech Republic.
Křemen, Jaroslav ; Hušek, Roman (advisor) ; Pelikán, Jan (referee)
This work deals with the demand for money theories and applications of error correction Models and VAR models for the demand for money in the Czech Republic. In the theoretical part of the work are discussed theory of demand for money, with an emphasis on Patinkins theory of demand for money and the wording of VAR models and error correction models. In the application part are applied VAR (1), VAR (2) models and error correction models on the demand for money in the Czech Republic. Data used in the work come from the information system CNB and the CZSO.
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