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Optimization of a a route for collecting waste with Traveling Salesman Problem
Trnka, Zdeněk ; Borovička, Adam (advisor) ; Pelikán, Jan (referee)
The Bachelor's dissertation deals with optimization of route designed for collecting communal waste of a company FCC Czech Republic, Ltd. Dissertation search for the most suitable method to solve the real-life example. So formed economic model is to be solved via Traveling Salesman Problem method, whose mathematical model, modifications and solutions options are described in detail in theoretical sections of the dissertation. Exact methods, which are suitable for smaller problem, and heuristic methods, which did not have to give optimal solution, can be used for solving the Traveling Salesman Problem. The Traveling Salesman Problem will be solved here with help of modeling software MPL for Windows. There will be also used two heuristic approaches - Nearest Neighbor algorithm and Savings method. Due to increasing efficiency, a modified Traveling Salesman Problem with Time Windows will be used and solved also through MPL for Windows. To close the dissertation, the result will be summarized and compare firstly among each other and secondly against current company route.
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Application of Vehicle Routing Problem in Geocaching
Frolík, Tomáš ; Skočdopolová, Veronika (advisor) ; Sekničková, Jana (referee)
Geocaching is a worldwide game that uses Global Positioning System (GPS). Most play-ers try to create a route to search for caches to make it as short as possible. The aim of the bachelor thesis is to design a model to be able to create the shortest route between individual caches under certain restrictive conditions within five independent circuits. The first part of the thesis presents the basic theoretical knowledge necessary for un-derstanding practical part. The second part is devoted to the basic terms of geocaching. Furthermore in the second chapter, the basic model, its individual variables, equations and evaluation are presented within the Vehicle Routing Problem. As a result, the mod-el is not entirely correct and needs to be expanded by a third index, which sets the conditions for each created circuit separately.
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An assignment of employees to clients in a small bussiness
Lebr, Karel ; Skočdopolová, Veronika (advisor) ; Fiřtová, Lenka (referee)
Employee assignment to clients in the service sector is often a problem with simple intuitive solution but with the growing number of employees and clients, the complexity of the problem is increasing. For these purposes it is possible to use methods of operational research, more specifically linear or non-linear programming. In the context of assigning something to something else, we can talk more specifically about the assignment problem. This thesis deals with the question of how to assign employees to clients according to their time preferences, taking into account the policy of the company surveyed. For this purpose, a model has been created and implemented in the form of a general assignment problem with upper and lower limits on the number of clients assigned to one teacher. The task also uses the minimax principle. From the studied models, that closest to the reality was chosen and was implemented on a real problem.
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Practical use of diet problem
Vítek, Lukáš ; Kuncová, Martina (advisor) ; Sekničková, Jana (referee)
The aim of this bachelor thesis is to formulate a mathematical model of linear programming problem, which will optimize the menu composition based on a required optimal amount of macronutrients. The goal programming approach is used to solve this problem. At first, the model which will only optimize diet with respect to nutritional values is formulated. After that this model is modified to provide a practically usable menu composition. Finally, the model is upgraded to three days model and more alternative ways are used to solve the problem. There is introduced theory of operational research and linear programming and basic recommendations on a balanced diet in the beginning of the thesis. Then these theoretical knowledges are used in a practical part. All models are formulated in MPL for Windows and solved by the solver Gurobi. The foodstuff database was created in the Microsoft Excel.
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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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Possibility of linking optimization models with logistics technologies
Vrbická, Jitka ; Kuncová, Martina (advisor) ; Fiala, Petr (referee)
This thesis focuses on linking optimization model of mixed linear programming with logistics technologies. To achieve the objective, the thesis is divided into two sections. The first section provides the necessary theory on linear programming and logistics. The second part focuses on the optimization model itself and its connection with the method JIT. This section also describes the application created in MS Excel spreadsheet, which then solves the issue. The application is linked with optimization softwares Lingo and MPL for Windows. The thesis conclusion demonstrates functionality of the application on an illustrative example and the optimization programs are compared based on the observed data. Based on the collected data, we can say that the optimization model is a suitable tool for the optimization of supply chains.
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Optimization in advertisement allocation
Do Chi, Linh ; Sekničková, Jana (advisor) ; Skočdopolová, Veronika (referee)
This thesis focuses on the optimization in advertisement allocation. The main aim of the bachelor's thesis is to propose a strategy, how to allocate an advertising for Penny Company s. r. o. that will maximize overall affinity by using quantitative methods. The thesis is divided into theoretical and practical parts. There are some indicators that specify measuring impact of advertising campaign and some basic types of media introduced to readers in the preliminary of theoretical section. Furthermore there are described basic concepts related to the linear programming together with methods and the ways of enrollment into system MPL for Windows which is later delivered itself as a troubleshooting. In the practical section there are two assignments of scheduling advertising which are solved by using MPL for Windows. In the end the results will be interpreted and verified.
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Optimization on assembly lines
Bark, Ondřej ; Borovička, Adam (advisor) ; Kuncová, Martina (referee)
The bachelor thesis focuses on modeling weekly planning of shifts considering numbers of working groups, corporation Continental Automotive Czech Republic ltd, where boosters are produced. The theoretical part involves definitions of elementary terms in mathematic programming, such as economic and mathematic model etc. Subsequently, there is a brief, concise description, possible approaches to optimization on assembly lines. In the second part the thesis evaluates a situation in a corporation and selects appropriate model or concept of solution -- generalized transportation problem or principle minimax. In the practical part of the thesis there have been created general models connected with MS Excel for a broader application in business practice followed by verification with real data. The entire analysis is created in MS Excel and optimization environment MPL for Windows with solver Gurobi 5.6.2.An important part of the thesis is comparison and interpretation calculated data with a real plan of production. The tracking week is the twelfth one in 2014.
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Recreational mathematics problem solving as an integer programing problems
Künzelová, Barbora ; Jablonský, Josef (advisor) ; Rada, Miroslav (referee)
The bachelor thesis deals with the solution of three selected recreational mathematics problems using discrete optimization. These problems are called Gridspeed Puzzle, Shifty Witnesses and Alien Tiles. The reader first learns the rules of these games of which are then formulated mathematical models that are integer in all cases. The first two games have one model and are being solved one way, but in game Alien Tiles are solved several optimization problems. All models are rewritten MPL modeling language in which they are solved by solver CPLEX. For all selected problems are found optimal integer solution, which is then described and explained to the reader. The solution results of the task Alien Tiles are finally compared and we are able to tell that one form of the desired outcome of the game is more difficult to calculate.
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