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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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Utilization of The Hungarian method for solution of Assignment problem
Petrovičová, Andrea ; Fábry, Jan (advisor) ; Borovička, Adam (referee)
The objective of this thesis is to present the basic of Assignment problem and also of the utilization of The Hungarian method. The theoretical part describes economic and mathematical model of problem. The paper describes in detail combinatorial optimization algorithm, The Hungarian method, which is considered one of the most efficient algorithm of solving process of Assignment problem. In the practical part, the algorithm is applied to create a new algorithm in VBA for MS Office Excel, which could be considered to be alternative optimization modeling software. Solution of tasks of great dimension and application of The Hungarian method to Transportation problem contribute to complex image of difficulty of the method.
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Use of project management during the reconstruction of primary school
Mikolajová, Zuzana ; Melechovský, Jan (advisor) ; Fábry, Jan (referee)
This bachelor's thesis deals with an application of project management during the reconstruction of a primary building. The theoretical part is focused on basic concepts of project management, models and methods. Practical advice on how such a project can be successfully accomplished will be included. The practical part is focused on establishing a real project in project's timeline with suitable software and costs analysis attached. The timeline can be described by Gantt chart, where critical path is provided. At the end of this thesis I will analyze the project, because the reconstruction was realized in the past.
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High school timetabling using linear programming
Kozárová, Barbora ; Skočdopolová, Veronika (advisor) ; Fábry, Jan (referee)
The school's schedule involves folding lessons within five working days, so that in each class were taught subjects required by the school curriculum in the correct number of hours and for each hour was assigned a teacher and a number of classrooms in which teaching will be realized. However, it is necessary to keep order in the resulting schedule avoid collision or vice versa unnecessary delays in the schedules of students and teachers in order to meet the conditions laid down by legislation and at the same time it was granted as much as possible the requirements of the management, teachers, or students or their parents. In this study it is proposed a mathematical model for the formation of a high school schedule that was created with the help of MPL for Windows and data provided by Gymnázium Chomutov.
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Heuristic Methods for Solving Generalized Vehicle Routing Problems
Kalendovský, Jan ; Fábry, Jan (advisor) ; Pelikán, Jan (referee)
The goal of the diploma thesis is to introduce and describe a heuristic method for finding a sub-optimal system of circuits in a generalized vehicle routing problem with time windows and time-dependent unit costs. Proposed method was built up on Clarke and Wright's savings method for the standard vehicle routing problem. Additionally, there has been described an algorithm for improving current solution via finding an optimal time harmonogram for a journey on each circuit within the found sub-optimal system of circuits.
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Training plan solved by assignment problem
Vejvodová, Tereza ; Borovička, Adam (advisor) ; Fábry, Jan (referee)
The aim of the bachelor thesis is to create the best training plan for the dancers on a weekly training camp. This is the assignment of categories to certain hours of training for every day on training camp. Each category has different requirements in terms of days of training and of course hours of individual trainings. This problem solves an assignment problem and for calculation is used optimization program LINGO. The most effective plan for dancers will be found with this program. This plan should be fair and should satisfy all categories. In the theoretical part is described linear programming, primarily assignment problem and integer programming. In the practical part is the theory applied in practice and it is created schedule of categories for each day of training camp.
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Heuristics for capacitated messenger problem
Přibylová, Lenka ; Fábry, Jan (advisor) ; Pelikán, Jan (referee)
This diploma thesis deals with static and dynamic capacitated messenger problem and its solving with heuristic algorithms. Different variations of the capacitated messenger problem were considered, with a single messenger or multiple messengers, with one depot or multiple depots in case of multiple messengers. Limited time for route realization was another modification that was considered. Modified nearest neighbour method, modified insertion method and modified exchange method were used to solve the problem. The main contribution of the thesis is deriving heuristics for described types of messenger problem and programming the algorithms in VBA (Visual Basic for Applications) in MS Excel. The results of computational experiments indicate that modified nearest neighbour method leads to better outcomes in static multiple messenger problems with a single depot, while modified insertion method is associated with lower values of objective function in static multiple messenger problem with multiple depots. Modified exchange method improves original solutions. Modified insertion method was approved for solving dynamic multiple messenger problems.
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Application of nutritional problem in use
Vojtíšková, Kamila ; Kuncová, Martina (advisor) ; Fábry, Jan (referee)
The bachelor thesis is focused on using nutritional problem in dog kennel of breed Tosa Inu, one of the molossoid dogs. The first part of thesis deals about theory of nutritional problem and its use in human and animal nutrition. The second part focuses on dog nutrition. Limits for nutrient values are made from the diet that is used in kennel and the influences of nutrients on dog's health and its correct development are also described in detail. Model of nutrition for kennel is realized in the third part of thesis and a global optimal solution with minimizing costs is found through program Lingo. The bachelor thesis also includes application of model in dog shelters and finding optimal nutrition for dogs of molossoid breed in shelters with minimizing costs of sponsors.
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Optimization of packages transport
Ptáčková, Michaela ; Borovička, Adam (advisor) ; Fábry, Jan (referee)
This bachelor thesis deals mainly with traveling salesman problem which belongs to the distribution problems and looking for its the best solution. The principle of the solutions of this problem is finding the shortest possible route that includes all of the prescribed addresses and returns to the initial location. Every location must be visited exactly once. There are numbers of modifications such as traveling salesman problem with time windows, courier service problem, dynamic traveling salesman problem and many others. We can solve these problems by using the systems to support modelling or using heuristic or metaheuristic methods. The thesis is divided into two parts, theoretical and practical. In the theoretical part the distribution problems are described, the traveling salesman problem in detail and selected algorithms of heuristic methods. The practical part is focused on the application of these methods which helps us to find the shortest possible route, which the PPL's employee would be able to manage during one day when he distributes packages. The solution is obtained by using an optimization system MPL for Windows, by application the nearest neighbour algorithm, the savings algorithm and the insert algorithm. In conclusion of the thesis all results are summarized and a mutual comparison of the calculation methods is performed.
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Metaheuristic optimalization for routing problems
Novák, Vít ; Fábry, Jan (advisor) ; Melechovský, Jan (referee)
Routing problems are ones of the most famous members of the group of the classical optimalization combinatorial problems. Travelling salesman problem and problems derived from it have been attracting mathematics and analysts, since they were firstly formulated, and accelerating a development of new methods and approaches that can be used for a wide range of another real-life problems. This thesis aims to demonstrate an usefulness and a flexibility of shown metaheristic methods. Results are compared with outputs of alternative algorithms or known optimal solutions where it is possible. To fulfill this goal the VBA application has been developed. The results of experiments are presented and the application is decribed in a second part of this thesis. A reader should be sufficiently instructed which way he could choose to solve similar types of problems
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