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Analýza trasování a vytíženosti manipulantů v lisovací hale
Bark, Ondřej ; Borovička, Adam (advisor) ; Fábry, Jan (referee)
The diploma thesis focuses on tracing in layout by handlers between assembly lines in new plant for corporation Continental Automotive Czech Republic ltd, where boosters are produced. The theoretical part involves definitions of logistics, supply chain, material flow and handling equipment. Furthermore, methods of mathematic programming and software equipment are described, such as quadratic assignment problem, knapsack problem, travelling salesman problem from graph theory. In the practical part the situation in corporation has been analyzed and the data prepared for further examination. Then layout of plant and internal processes are evaluated and an appropriate model or concept of solution is selected. Subsequently, application in MS Excel is created with support of VBA scripts (3 kinds of layouts). The user manipulates with application followed by Solver for implementation of a new solution into practice. Finally, the models are interpreted and verified by Lingo. The focus of the thesis is the design of a layout change of a new plant including the description of tracing.
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The multiple knapsack problem in use
Procházková, Lucie ; Sekničková, Jana (advisor) ; Suchánková, Tereza (referee)
In the area of integer linear programming problems is placed the knapsack problem, including its modifications. Among them is the multiple knapsack problem which is the subject of this thesis. In connection with the interpretation of results is necessary to extend the knapsack problem to integer conditions that are most often transformed into a bivalent conditions. This greatly increases the computational complexity of these tasks. Despite the fact that solutions exist for the exact algorithms, often in the calculation of some large problems can not be used. Approximate and sufficiently accurate results can be achieved by using heuristics and other techniques that have been created for this purpose. Subchapters in the first part further describe the variation of the knapsack problem, in the second part subchapters followed, and present some possible use in practice.
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Graph theory – an alternative method of solving LP problems
Hrabovská, Michaela ; Šindelářová, Irena (advisor) ; Chýna, Vladislav (referee)
This bachelor thesis analyses an example of an alternative method of solving selected linear programming problems using graph theory. These alternative methods are explained not only theoretically, but also illustrated on the practical examples. For comparison, there is a theoretical description and also practical solution of selected problems with using linear programming stated in the text. In the introductory part of the thesis, the theory of operations research is briefly discussed. The selected problems are: knapsack problem, transportation problem, assignment problem.
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Optimal composition of groceries for mountain trip
Fesenko, Anastasiya ; Kalčevová, Jana (advisor) ; Flusserová, Lenka (referee)
This work is aimed towards the application of knapsack problem in practical example of packing of groceries for mountain trip. The knapsack problem is one of the tasks of integral programming; those are the models that can only variably accept the integral value. The solutions of integral tasks are usually very meticulous. That is why for their solution special algorithms were created, which are capable of discovering an integral solution of such tasks, for example, branch and bound method, Balas method etc. These types of algorithms are defined in the first part of this work. While writing this thesis a considerable emphasis was put into application of its result in practice. Hence, for achieving applicability practical tasks are solved from various angles and therefore various aims have been set forth in each solution option. The results of each option are interpreted and then the differences are explained.
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The multiple knapsack problem
Černý, Vít ; Kalčevová, Jana (advisor) ; Suchánková, Tereza (referee)
The knapsack problem is one of the classical operations research problems. It belongs to the category of integer linear programming problems and is most often formulated as a binary problem. This thesis describes different categories of the problem and also some methods for finding their solution. Although there are precise algorithms for finding reliable optimal solution, some of the knapsack problems are so large that it would be impossible to follow the exact algorithms. Therefore, more complex knapsack problems belong to the complexity class of NP-complete. Yet there are a variety of heuristics and methods developed, which can lead to a sufficiently good solution in a relatively short time and relatively simple way. This paper focuses particularly on one of the problems described, the multiple knapsack problem. It is showed on a practical example how the problem can be solved.
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The Multi-Dimensional Knapsack Problem
Ficová, Pavla ; Kalčevová, Jana (advisor) ; Černohous, Roman (referee)
This work deals with multi-dimensional knapsack problem. Knapsack problem coincides with the category of integer linear programming. Thanks to the necessity of integer result it used to be more difficult to find the solution, by meeting all limitations. A lot of statisticians and mathematicians from all over the world are engaged in inventing an exact algorithm for calculation of these problems. As at now, there have been various accesses and heuristics concerning how to solve these problems or at least how to get as close to the optimal solution as possible. Problems with many variables are impossible to solve by hand calculations, the model is too complex and number of iterations is really high. Extensive exercises can be solved by advanced software in several minutes or longer. This work is trying to describe the problems, clear up and show practical application of knapsack problem in a real situation.
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