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Testing software for mixed integer programming
Kmetonyová, Daniela ; Jablonský, Josef (advisor) ; Kalčevová, Jana (referee)
Táto diplomová práca porovnáva tri vybrané optimalizačné softvéry z hľadiska rýchlosti výpočtu a presnosti riešenia úloh zmiešaného celočíselného programovania a užívateľskej prístupnosti ovládania softvéru. Ďalej obsahuje popis fungovania a použité postupy pri výpočte jednotlivých testovaných softvérov, a to hlavne s dôrazom na riešenie zmiešaných celočíselných úloh. Testované boli softvéry ? CPLEX 10.1, Xpress 18.00 a MOSEK 5.0. Na testovanie boli použité úlohy z knižnice MIPLIB 2003.
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Practical application of cutting problem with atypical targets
Marcineková, Petra ; Kalčevová, Jana (advisor) ; Šmídová, Milada (referee)
This bachelor work deals with one of the linear programming problems, the problem of optimal dividing of the material. The typical targets of these problems in classes is to minimize waste and minimize the material used. The aim of this work is the formulation of the unusual targets of this problem. These atypical targets include minimizing the number of cuts, counting waste nicked by cutting-off or to ensure a certain proportion of final products. Part of this work is the practical application of those unusual modifications of cutting problem.
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Těžba v Predator-Prey modelu
Chrobok, Viktor ; Lagová, Milada (advisor) ; Kalčevová, Jana (referee)
The paper is focused on the Predator-Prey model modified in the case of harvesting one or both populations. Firstly there is given a short description of the basic model and the sensitivity analysis. The first essential modification is percentage harvesting. This model could be easily converted to the basic one using a substitution. The next modification is constant harvesting. Solving this system requires linearization, which was properly done and brought valuable results applicable even for the basic or the percentage harvesting model. The next chapter describes regulation models, which could be used especially in applying environmental policies. All reasonable regulation models are shown after distinguishing between discrete and continuous harvesting. The last chapter contains an algorithm for maximizing the profit of a harvester using econometrical modelling tools.
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Postoptimality changes in the transportation problem
Plechatá, Zuzana ; Lagová, Milada (advisor) ; Kalčevová, Jana (referee)
The aim of this bachelor thesis is to outline a postoptimality changes in the transportation problem. Postoptimality analysis evaluates how may be the optimal solution affected by an additional changes. I will point out procedures which are using in cases of the postoptimality change in the price coefficients and change in the right-hand-side values for constraints. Described methods will be applied to the practical examples.
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Analysis of transportation problem with bounded variables
Klasová, Petra ; Kalčevová, Jana (advisor) ; Šmídová, Milada (referee)
This bachelor thesis introduces the transportation problem with bounded variables, methods design and practical application of these methods on fictive data. The examples demonstrate the algorithm of optimal solution calculation. This thesis describes the modification of the north-west corner method, index method and Vogel's approximation method for problems with bounded variables, as well as the distribution and modified distribution method.
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Optimalizační server NEOS
Tabach, Arnošt ; Jablonský, Josef (advisor) ; Kalčevová, Jana (referee)
Tato práce se zabývá využitím serveru NEOS při optimalizačních výpočtech. Jejím cílem je ?ověřit možnosti serveru NEOS a předvést praktické možnosti, zejména pro potřeby výuky. ?Omezuje se na spojení serveru NEOS s optimalizačním systémem AMPL. Obojí je teoreticky ?popsáno v první části, v druhé jsou obsaženy praktické ukázky výpočtů. V závěru jsou stručně ?rozebrány výhody a úskalí při využití serveru NEOS. ?
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Assignment problem
Partynglová, Soňa ; Lagová, Milada (advisor) ; Kalčevová, Jana (referee)
This thesis is describing one of the most popular method (Hungarian method) for solving the assignment problem. This type of problem is usually just defined by most the writers instead of it's real treatement. The main target of this thesis was to resume the knowledge of this problem, to define it carefully and to use Hungarian method for finding the best solution. This thesis also shows the differences between solving this problem by minimalisation or maximalization of the function of effectiveness and this thesis also shows how to solve the unbalanced tasks.
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Practical aplication of diet problem
Harák, Tomáš ; Kalčevová, Jana (advisor) ; Šmídová, Milada (referee)
I have decided to try solve the question if it is possible to eat healthy at McDonald's fast-foods. I will try to do this with my skills and knowledge of linear programming. I will try to find optimal solution by minimalizing total cost of food. If I don't find the solution, I will try to answer "Why?"
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