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Postoptimality changes in trasportation problem
Hesounová, Kristýna ; Lagová, Milada (advisor) ; Kalčevová, Jana (referee)
This bachelor thesis deals with postoptimality changes in the transportation problem. Postoptimality analysis evaluates how can be optimal solution influenced by an additional changes in setting. The theory, which is necessary for understanding these questions, is mentioned first. Then are clarified methods, which are using in cases of changes in rigt-hand-side values for contraint, changes in value of price coefficient and changes in number of constraing. These changes are demonstrated on examples.
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Solving of integer problems by dynamic programming
Polonyankina, Tatiana ; Kalčevová, Jana (advisor) ; Lagová, Milada (referee)
Optimalization problems with integer requirements on the variables occurs in real life very often. Unfortunately, finding optimal solutions to such problems are often numerically very difficukt. The work describes several possible algorithms for solving linear integer problems. The reader is also familiarized with the method of dynamic programming and the principle of optimality. This is demonstrated in a practical example of a knapsack model where the calculation is done using tables. The goal of this work is to apply the knowledge from the application of dynamic programming on a typical linear integer problems, namely on the problem of material separation, and thus show the algorithm of calculating integer problems. Finding the optimal integer solution is accomplished in two ways: by the classical method of spreadsheet tables and by the simplified method of using Lagrange multipliers. In the conclusion there are summarized the advantages and disadvantages of solving technic.
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The Generalized Distribution Problem Approach
Fuksová, Lucie ; Lagová, Milada (advisor) ; Kalčevová, Jana (referee)
The generalized distribution problem is task from linear programming approach which belongs to the distribution problems with specific mathematical model. For solution this problems we need to use another methods than the universal simplex method. A typical example is the transportation problem. The generalized distribution problem differs from it only in a small difference in mathematical model, but compared to the traffic problem has computational difficulties. To build the model and its solution is necessary to calculate the transmission coefficients, the so-called "performance factors". This work will prepare the answers for problem formulations and mathematical model and will describe the procedures that can solve problems of similar type. Methods used in the thesis are modified distribution method and the simplex method. To calculate solutions will be used the optimization software Lingo.
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Generation of linear programming tasks
Serbová, Eva ; Lagová, Milada (advisor) ; Kalčevová, Jana (referee)
Bachelor thesis deals with generation of linear programming (LP) tasks for academic education purposes. In the beginning part of thesis there are briefly described methods for pseudorandom numbers generation and basic characteristics of linear programming methods. Chosen and realised procedure of LP tasks generation is based on inverse algorithm. Inverse algorithm proceeds from resultant values backward to input ones. This process provides generation of LP tasks. All tasks are comparable in terms to calculation difficulty. This method is appropriate for manual calculating and is suitable for practicing and testing of students. Part of the text contains brief description of the application program LinPro which is used successfully in education of lessons accredited by Department of Econometrics at University of Economics in Prague. The thesis is finished by couple of sample models.
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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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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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