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Collection of mixed waste in the city of Poděbrady
Bilá, Tereza ; Fábry, Jan (advisor) ; Pelikán, Jan (referee)
Increasing waste production is the reason why it is important to focus in more detail on profitable and cost side of waste economy. This diploma thesis deals with the area of garbage collection as a fundamental part during garbage their cumulation in a particular location and follow-up liquidation or preservation. At first the theoretical background of Chinese Postman Problem is described as a cornerstone for garbage collection models. Extensions of this problem have to be considered to be closer to reality. Then waste management in the city of Poděbrady is thoroughly described. In the final part of diploma thesis aforementioned theoretical models are applied on real data obtained from the city of Poděbrady waste department. Heuristic algorithms are an essential part of thesis as a replacement of optimizations models that cannot be used in some cases due to high requirements on computational time.
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A Randomized Heuristic for the Capacitated Postman Problem
Rýdlová, Lenka ; Pelikán, Jan (advisor) ; Fesenko, Anastasiya (referee)
Graph theory is a large mathematical discipline. Chinese postman problem falls under category of arc vehicle routing problems. Chinese postman problems are very extensive and difficult to calculate in practice. They belong to NP-hard problems. For this reason, heuristics are proposed to provide acceptably good solution in polynomial time. The focus of this thesis is to propose a randomized heuristic which does not follow deterministic rules but is ruled by random. Monte Carlo simulation is launched to find the best solution. Heuristic is formulated for undirected capacitated rural postman problem. It is programmed in VBA and validated on testing problems. At the end of the thesis is a case study about municipal garbage collection.
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Modified Chinese Postman Problems - Experiments
Jelínek, Tomáš ; Fábry, Jan (advisor) ; Pelikán, Jan (referee)
This master's thesis describes modified Chinese Postman Problems. These Problems are solved by (mixed) integer linear programming. The modified problems and also used approach (integer programming) belong at least to the NP complexity class. The thesis analyzes, compares and estimates computational complexity of each model. Based on this analysis, usability of described models for solving real-life problems is deduced. The models are focused on problems in urban environment. Therefore, it is possible to apply these models on problems like optimization of a waste collection or road maintenance. Graph and problem generator is programmed for purposes of this thesis.
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Optimalization of Police Department solved by Mathematical Modeling
Podlešák, Ondřej ; Suchánková, Tereza (advisor) ; Fábry, Jan (referee)
The main goal of this Bachelor's Thesis is to optimalize the function of Police Department using Mathematical Modeling. The Thesis is divided into three chapters. First chapter is summing up the graph theory and theoretically describes the two solved problems: Chinese postman problem and Travelling salesman problem (CPP and TSP). Second chapter describes process of creating general model capable of finding optimal solution for the two mentioned problems. Third chapter then applies knowledge described in first two chapters on a practical problem and finds a solution. This solution is an ideal path for policeman.
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Optimization of Distribution of Advertising Brochures
Naglová, Martina ; Fábry, Jan (advisor) ; Jágerová, Tereza (referee)
The aim of the thesis is to determine the optimal route for delivery of advertising brochures. To address this problem, Chinese Postman Problem is used. In contradistinction to other works, this practical work is modified by inclusion of the streets width and number of houses into calculation. The postman can go through the street by two different ways. There is undirected graph with unrequired edges in the practical work. Because of extensiveness of this work it was necessary to use software products, specifically Lingo. It is described Chinese Postman Problem, its mathematical model, history and modifications and basic concepts of theory of graphs, where Chinese Postman Problem belongs to.
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Optimizing of municipal waste collecting
Maxa, Jan ; Fábry, Jan (advisor) ; Jágerová, Tereza (referee)
The aim of this work is to determine the optimal route in the city for municipal waste collection for garbage wagon. To address this problem, the Chinese postman problem is used. Introductory chapter describes some basic terms from the theory of graphs, where the Problem of Chinese postman belongs to. Another chapter is devoted to description of the Chinese postman problem, including ways of solving in the undirected and directed graphs. The following chapters describe all types of streets in our problem, mathematical model and interpretation of the optimal solution. Example is solved with optimizing software LINGO.
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