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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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Origin of linear programming as a scientific discipline
Fišmon, Petr ; Šindelářová, Irena (advisor) ; Kuncová, Martina (referee)
This thesis deals with the origin and extension of linear programming. It describes various influences that have participated in its formation. The first part of thesis describes military influences, which stimulated governments of great powers to support mathematical modelling and development of linear programming. Next point of the bachelor paper is development of general linear model that was based on economics models. The thesis deals with mathematic theory, which gave the foundation to the Simplex method and with computer technology, which was able to solve linear models and put them into practice.
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Analysis of reduced and shadow prices in linear programming problems with lower and upper bounds
Průšová, Lucie ; Jablonský, Josef (advisor) ; Kořenář, Václav (referee)
Abstract Title: Analysis of reduced and shadow prices in linear programming problems with lower and upper bounds. Author: Lucie Průšová Department: Department of Econometrics Supervisor: doc. Ing. Milada Lagová, CSc. This thesis deals with linear programming problems with additional requirements that values of variables are greater or lower than a specified bound. Where applicable, the variable is limited on both sides. These values are called the upper and lower bounds. Lower bound can be a minimum required number of manufactured products and upper bound a maximum permissible quantity of a substance in the mixture. The thesis contain a formulation of original LP problems with lower and upper bounds which are solved by standard simplex method and by its modification for bounded variables. The aim of this study is to analyze and compare the reduced costs and shadow prices in the mentioned class of problems. At the end there will summarize the results of this work.
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