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High school timetabling using multicriteria linear programming
Žítek, Jan ; Skočdopolová, Veronika (advisor) ; Kuncová, Martina (referee)
The theme of this thesis is high school timetabling. The built mathematical model is based on bivalent programming. The model uses multicriteria linear programming too, because a timetable has to fill legal and school's requests and student's and teacher's wishes. Firstly, there are given theoretical basics. Then there is described economic model with school's characteristics and it continues by mathematical model. For optimization, tool MPL for Windows with using Gurobi. Finally, export of optimization is transferred using VBA to form for end users.
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Route optimization for the parcels distribution
Ptáčková, Michaela ; Borovička, Adam (advisor) ; Čížek, Ondřej (referee)
This thesis deals with optimization problems of the parcels distribution. This issue can be solved on the ground of traveling salesman problem whose mathematical and economic model, including their modifications, are presented in the theoretical part of the thesis. We can solve these problems by using exact methods, heuristic and metaheuristic algorithms. In the theoretical part are described traveling salesman problem, traveling salesman problem with time windows, traveling salesman problem with multiple time windows and dynamic traveling salesman problem including possible ways of solution. In the practical part we can find application of problems on the real example, when we are finding the shortest possible route for the PPL's employee under different assumptions. The solution is obtained by using solver Gurobi within the modelling system MPL for Windows. In conclusion of the thesis the results are summarized and models are compared with each other.
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Goal Programming Models: Theory, Applications, Software Support
Skočdopolová, Veronika ; Jablonský, Josef (advisor) ; Brezina, Ivan (referee) ; Šubrt, Tomáš (referee)
Goal programming is an approach for solving decision problems. The aim of this doctoral thesis is to show the practical use of this approach for solving real problems. The first chapter brings a brief introduction to multicriteria decision making. The second chapter is devoted to goal programming, its history, theory, criticism and also to its practical applications. The third chapter deals with description of a model for optimisation of white mass production. This model utilises the goal programming principle to deal with measuring deviations of raw materials' composition. A part of this chapter is a presentation of OPTIPROT, an application that implements the mentioned model. In the fourth chapter there are described three mathematical models for timetabling at a department level; two multistage models and one complex model. All three models are formulated utilising goal programming. In this chapter there is also described an application that implements the complex model for timetabling.
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Optimization of Distribution of Advertising Brochures
Svobodová, Veronika ; Fábry, Jan (advisor) ; Pelikán, Jan (referee)
The goal of my thesis is to optimize the route for replacement of bus schedules in Prague. This task deals with the role of the Traveling Salesman Problem, which belongs to the class NP-hard problems. The solution is numerically very difficult and is gained by using the system LINGO and by using optimization solver Gurobi. The task is modified so that the total time traveled by vehicles does not exceed the specified value. In my thesis I first characterize the problem of replacement of bus schedules. Following chapter is devoted to the role of Traveling Salesman Problem, its history, definitions, problems to solve, possibilities of solution and modification of the tasks on Traveling Salesman Problem with more vehicles. The last chapter deals with the procedure for resolving and results of the problem.
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