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Optimalization of distribution process in trading company
Scigel, Pavel ; Jablonský, Josef (advisor) ; Kořenář, Václav (referee)
The thesis deals with distribution problems and their methods for their solution. They belong to one of the most often used optimization models in practice. The thesis describes background for using modelling support systems LINGO and MPL for Windows. The modelling languages allow solving all problems described in the theoretical part including the travelling salesman problem and the vehicle routing problem. There are described basic heuristic methods for problems with higher number of variables in this work as well. The thesis includes the description of a real situation for which it is possible to apply travelling salesman problem or vehicle routing problem models. It is a complex problem which cannot be solved by exact methods but heuristic methods must be used. The problem is going to be solved by means of MS Excel together with Visual Basic for Applications using the heuristic method of nearest neighbour.
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Collection of Solved Linear Programming Problems
Ďuricová, Alexandra ; Šindelářová, Irena (advisor) ; Kořenář, Václav (referee)
The target of this bachelor thesis is to build new examples of linear programming. The examples in this work include all the formalities which are necessary for the correct interpretation. The entering tasks designed are based on real problems and consist of as much real values as possible. The work is divided into nine chapters and eight of them represent one area of linear programming. The first chapter is a short introduction into the theory of linear programming. The second chapter consists of two parts representing integer and non-integer programming. This chapter is the largest and contains 9 examples. The following four chapters consist of examples of non-integer programming and the last three chapters contain examples of integer programming.
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Optimization production for AKT
Mahnel, Petr ; Kuncová, Martina (advisor) ; Šindelářová, Irena (referee)
This thesis aims to provide a reader with practical example of optimization achieved using the Lingo software. The main focus is improvement of efficiency and shortening of a production process in AKT, a company engaged in production of car parts. It is a software, which accommodates needs of the company as well as production requirements. The theoretical part is focused on detailed description of methods and procedures used in a practical part. These methods should help the reader to understand a nature of formulas relevant for the subject. Practical part focuses on the optimization using data obtained from the company AKT, evaluation of the data and subsequent consultations with a manager of production, followed by the assessment of practical relevance for the production.
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Evaluation and decomposition efficiency using Malmquist productivity index
Skočdopol, Petr ; Dlouhý, Martin (advisor) ; Chrobok, Viktor (referee)
At first, the basics of microeconomics from the perspective of companies, effectiveness and methods of its measurement and the most important information on the distance function this thesis, are shown. It also contains the development of the Malmquist productivity index. The aim of this work is the description of this index and its components. Indicate how these values are calculated and what expressed. Secondary objectives are to introduce different variants of Malmquist indexes and their use. Four models are used for calculating individual components of the Malmquist productivity index. These are the DEA models, Aigner-Chu, Stochastic production frontiers and Stochastic activity analysis. The first three in this work are described in detail. In conclusion is an illustrative example of calculation Malmquist productivity index using DEA models. For the calculation I used the program Lingo.
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Solving the Battleship Solitaire puzzle as an integer programming problem
Přibylová, Lenka ; Jablonský, Josef (advisor) ; Fábry, Jan (referee)
The bachelor thesis deals with the Battleship Solitaire puzzle. It introduces the history and the rules of this puzzle, which are thereafter used to formulate the puzzle as an integer programming problem. Two mathematical models based on different approaches are created, a cell-based model and a ship-based model. In order to determine whether a puzzle has a unique solution an objective function is added to each model. Both models are developed in LINGO modeling language and tested with different grid sizes. The test results show that even though the ship-based model uses fewer variables and constraints, it is too demanding in terms of data processing. It results in longer solving times and the model fails to find a solution for larger grids. Solving the problem using the cell-based model is significantly faster. The solution was found even for larger grids, though the solving time was very long.
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Analysis of the cereal food products using mathematical modelling
Grygárková, Eva ; Jablonský, Josef (advisor) ; Škulavíková, Štěpánka (referee)
The bachelor thesis deals with nutritional values of cereal food products from three companies (Nestlé, Bona Vita and Emco). In the first part of the thesis linear programming models are described. The next chapter deals with the characteristics of the real situation in which Guideline Daily Amounts and nutritional values of specific cereal food products are set, and economic and mathematical model is formulated. The last part is devoted to numerical experiments. At first, the models are solved in MS Excel 2007 and then some of them are analysed in LINGO modelling system. The main aim of the thesis is to determine whether cereal food products are healthy and nutritious in terms of their nutritional values. The proposed models determine the individual portions of cereal food products consumed per day using the minimum costs that are spent for the purchase of the products.
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