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Travelling around Vietnam-application of Travelling Salesman Problem
Pham, Thuy Trang ; Dlouhá, Zuzana (advisor) ; Fábry, Jan (referee)
The circular traffic problem, also known as the Travelling Salesman Problem (TSP) belongs to a group called distribution problems, which is one of the significant group of linear programming. These tasks can be used in many applications areas such as production planning, logistic or travelling. This thesis deals with the application of TSP or its modification to find the optimal route among selected Vietnamese destinations. The aim is to find the best circuit among 20 places out of 37 considering the cost and time. The first chapter concentrates on the general theory of linear programming including the description of economical and mathematical models of the selected distribution problems. The main part of this thesis focuses on The Travelling Salesman Problem itself and its practical application
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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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Planning a holidays in Europe with using goal programming
Otarbayeva, Zhamilya ; Skočdopolová, Veronika (advisor) ; Kuncová, Martina (referee)
In this thesis I consider possibility to spend my vacation in one of the three countries: Spain, France, Italy. In each country I chose ten cities, which I would like to visit. I will use Travel Salesman Problem to decide the best route inside each country according to three criteria: Cost, Minutes and Transport. There is also a possibility to choose the type of transport: train or combination of train and airplane. Also I will use Weighted goal programming and Chebyshev goal programming to optimize all criteria simultaneously. In the end I will use multiple -- criteria decision analysis to compare results. According to three methods (ORESTE, ELECTRE III, TOPSIS) I will choose one of the states for my vacation. I will make all calculation in program MPL and in Excel using solver SANNA.
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Optimalization of the beer distribution in Jesenicko
Krčmář, Pavel ; Fábry, Jan (advisor) ; Suchánková, Tereza (referee)
The thesis deals with application of models of routing problems on a real problem, beer distribution in Jesenicko region provided by Viden plus, a.s. The goal of the thesis is to optimize daily distributional routes for two vehicles with different capacities. Total distance has to be minimized respecting time and capacity limits. In case the optimal solution is not found, sub-optimal solution will be accepted. Solutions are calculated with use of the optimization software LINGO and some heuristic methods. Models of travelling salesman problem and vehicle routing problem are used to find the solutions. Results are compared to the current state of distributional routes in conclusion of the thesis.
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System for solving distribution problems of LP – LINGO/Excel interface
Krčál, Adam ; Jablonský, Josef (advisor) ; Zouharová, Martina (referee)
Discrete problems of linear programming, i. e. problems with integer or binary variables, have a great amount of real-life applications. Among distribution problems, belong many different kinds of problems with discrete character -- transportation problem, container transportation problem, allocation problem, assignment problem, plant location problem, traveling salesman problem etc. In this work the theoretical aspects of chosen types of problems are explained and then an application in Microsoft Excel 2010 environment is created. For that purpose programming language VBA is the key instrument. The application cooperates with two different optimization systems -- the Solver add-in in Excel and professional optimization system Lingo. Functionality of the application is thereafter tested on some examples.
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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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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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Analysis of Municipal Waste Processing System a particular city
Bielová, Veronika ; Černá, Anna (advisor) ; Přibyl, Vladimír (referee)
Bachelor thesis discusses basic terms of waste management, focuses on collection and transport of municipal waste and includes possible ways to optimize the collection and transport of waste. Main part describes collection and transport of municipal waste in particular town and in addition also examines whether the company has optimal waste collecting routes or not through travelling salesman problem.
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Heuristic methods for messenger problem
Kobzareva, Maria ; Fábry, Jan (advisor) ; Pelikán, Jan (referee)
This work describes static and dynamic problems with one messenger or multiple number of messengers and suggests a possibility of solving such problems with modified heuristic methods. To solve messenger problem, modified nearest neighbor heuristic, modified insertion heuristic and modified exchange heuristic are used. The main contribution of this work are applications, developed in MS Excel, programmed with Visual Basic for Application, that can solve static and dynamic problems with one messenger or multiple number of messengers and that could be beneficial for companies that do business in messenger services.
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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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