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Timetabling on Business College
Marešová, Iva ; Jablonský, Josef (advisor) ; Skočdopolová, Veronika (referee)
This thesis deals with a creation of a timetable on Business College. In the first part the areas in which we can encounter scheduling are introduced, because timetabling undoubtedly belongs to scheduling tasks. Then the linear programming theory is explained. With its help a model for a timetable is made. The assignment problem, which forms a basis for timetable creation model, will be mentioned. We cannot imagine all that without the support of computers. That is why one chapter is dedicated to useable computer programs. The next chapter discusses didactics and its requirements for a good timetable. These requirements are then taken into account in an application chapter. Fundamental part of the thesis is the creation of the timetable for real Business College, taking into account all important conditions. At the end of this thesis a mathematical model is introduced which is suitable for creating timetables for twenty-four classes of this school.
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The choir’s tour planning - an application of travelling salesman problem
Marešová, Iva ; Skočdopolová, Veronika (advisor) ; Šindelářová, Irena (referee)
This thesis deals with planning a journey for a choir's tour by means of different methods of mathematical modelling. The first approach is the application of a travelling salesman problem. The study aims to find the shortest closed cycle which will give us an optimal solution. In the case which is solved in this thesis the model of the travelling salesman problem is partly modified because our goal is to choose only half of all the places which are the most effective for us. The thesis focuses on the application of those methods which give us only an approximate solution, particularly the method of the nearest neighbour and the method of change replacement. The first part of the thesis is devoted to the theory dealing with linear programming, distribution problems, heuristic methods and computer programmes for optimization. In the next part the discussed methods are applied to the concrete case in which the journey for the tour is planned. At the end of this thesis there are mentioned modifications which could be solved in this type of problems.
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