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Postoptimization analysis in parametric programming
Ten, Anastassiya ; Sekničková, Jana (advisor) ; Skočdopolová, Veronika (referee)
This bachelor thesis deals with postoptimality analysis of parametric programming problems. Parametric programming problem is problem, where some of the coefficients are not constant but depend on one or several parameters. Postoptimality analysis explores intervals of stability of coefficients in an initial solution and impact of additional changes in the assignment of the problem. Mentioned theory explains main terms and methods, which were illustrated on practical examples.
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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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Alternative rules for determining pivot columns and pivot rows in the simplex method
Leontiev, Andrey ; Kalčevová, Jana (advisor) ; Skočdopolová, Veronika (referee)
In my thesis I tried to describe the problems of choice of a pivot in the simplex method. The first part is devoted to the mathematical model of linear programming and simplex method in general. Here are explained the key concepts and principles of this method. There is the description of alternative rules for choosing a pivot using the simplex method in the second part. The description of each method is supported by example. I emphasize here the proofs of finite algorithm for each rule. In the last part of my thesis I have placed my own examples to show the different effects using different methods.
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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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Optimization of production and distribution in bakery
Bilá, Tereza ; Kalčevová, Jana (advisor) ; Flusserová, Lenka (referee)
The subject of this bachelor thesis is optimization of production and distribution. The thesis aims to introduce the production problem in the case that the production limits are known and present its solution using a modified simplex method with lower or upper limits. The vehicle routing problem with one distribution centre and one vehicle will then be introduced. In the practical part of the thesis, these methods are applied in real-life data from the Martínek bakery business. The optimal production, which is targeting to maximize the profit under the given terms, and the optimal distribution from the bakery to shops, will be determined. At the end of the thesis, there is an evaluation of the given targets.
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Using linear programming to solve Markov decision processes
Dotlačilová, Petra ; Kořenář, Václav (advisor) ; Fábry, Jan (referee)
The aim of this bachelor thesis is to develop and describe how to solve Markov decision processes with alternatives by using the methods of linear programming. The theoretical part describes Markov decision processes. The practical part builds and describes the mathematical model of linear programming processes for Markov decision processes with alternatives. The method used for the calculation of the processes is described with the help of a simplex method. The last section of the practical part studies how the optimal solution of the linear programming is influenced by the postoptimalization changes which modify the probability and revenue properties of the processes.
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Criss-cross method
Papež, Jan ; Kalčevová, Jana (advisor) ; Šmídová, Milada (referee)
This thesis describes the criss-cross method, which solves the tasks of linear programming and does not need primar or dual feasibility of the basis. At first, the single-phase simplex method, that needs primal feasibility, gets described. After that, we describe the dual simplex method, which needs dual feasibility. The criss-cross method combines both of these methods. All of mentioned methods are explained and demonstrated in several examples.
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