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Mathematical models for transportation problems
Votavová, Helena ; Novotný, Jan (referee) ; Popela, Pavel (advisor)
The thesis deals with modelling and solution techniques for the selected transportation problems. Firstly, historical remarks and application-related comments are introduced. Then the selected transportation problems are defined and mathematical programming and graph theory concepts are utilised to model them. The travelling salesman problem and suitable algorithms are under focus. The original implementation in GAMS and Python is discussed. Algorithms have been tested for the instance based on the set of 73 towns in the Czech Republic. Finally, the test results are evaluated and compared.
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Vehicle routing problem in practice
Tuan Hoang, Anh ; Dlouhá, Zuzana (advisor) ; Kuncová, Martina (referee)
Nowadays, one of the most widely used optimization problem is a travelling salesman problem. That is only the basic model, which is modified by various restrictions and enlargements. In the first part of this bachelor thesis we will focus on theory of distribution problems and their solutions. On the other hand in the second part we will apply the knowledge from the first part to the real task, which requires modifications. We will use the data of the supply company that delivers their orders in Prague with the limited capacities of the vehicles. We will find out the differences between minimizing the total distance and minimizing the total time for delivery, as the distance and time are not linearly dependent. It will be needed to decide, where will be an optimal location for opening the second branch. To solve this tasks, we will not use only heuristic methods for manual calculation, but also optimization software.
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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 medicaments distribution from Movianto s.r.o. Warehouse
Šimáně, Čestmír ; Kuncová, Martina (advisor) ; Fábry, Jan (referee)
Nowadays, when great emphasis is put on cost savings, transport optimization is necessary part of every company life in which transportation costs produce significant part. There are optimization methods and possibilities presented in this thesis. In the first chapter there are explained methods such as the travelling salesman problem, the vehicle routing problem, the multiple vehicle routing problem and the split delivery vehicle routing problem and then the reader gets to know the heuristics methods in the chapter two where description of the nearest neighbour method, Clarke-Wright method and split delivery heuristic is mentioned. In the last but one chapter author applies previous methods on concrete distribution arranged by Movianto Česká republika s.r.o. on 5th September, 2013. Based on gained outputs, analysis and comparison of results (including the original distribution) are provided in the fourth chapter. Obtained results of analysis lead to recommendation on how the company should plan its future distribution.
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Optimization in a maintenance service of tram switches
Marková, Petra ; Fábry, Jan (advisor) ; Borovička, Adam (referee)
The goal of this work is to evaluate the effectiveness of the current existing route plan and the schedule of working hours for employees of a maintenance service of tram switches. In addition, the work is aimed at proposing a plan of individual routes for servicemen in the case of a reduction of number of employees in order to save salary costs. The problem is formulated as the travelling salesman problem, the most frequently used scheme for solving circular traffic problems. Specifically, we solve the problem of several salesmen with one common depot and apply methods of linear programming. Several different models were tested in order to achieve the best improvement. Because of NP-hardness of the problem, we applied the heuristic algorithm of the nearest neighbour. We found a solution similar to that of the existing maintenance plan but with more uniform route time durations for individual service workers. The proposed solution eliminates large fluctuations of route times for individual servicemen. We also propose a route plan for a reduced number of servicemen of tram switches with an acceptable change of working hours.
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Optimization of meter reading route
SVAČINA, František
This thesis deals with the creation of software that will calculate and display the optimized route. The aim was to create software running on the Windows operating system. The basic purpose of the application is to find the most suitable route for the movement of workers, to visit all entered places.
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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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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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