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Graph Theory in Economic Practice
Geško, Dávid ; Půža, Bedřich (referee) ; Novotná, Veronika (advisor)
In Bachelor’s thesis we deal with Traveling salesman person problem. In theoretical part are introduced basic terms of graphs theory and methods to solve Traveling salesman person problem. Practical part draws a comparison among efficiency of several methods solving this problem in environment of real world examples. In summary analysis are these methods evaluated and consequently chosen and implemented most effective method for company, which want to use it to determining most optimized tours for distributing goods.
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Graph Theory in Economic Practice
Geško, Dávid ; Půža, Bedřich (referee) ; Novotná, Veronika (advisor)
In Bachelor’s thesis we deal with Traveling salesman person problem. In theoretical part are introduced basic terms of graphs theory and methods to solve Traveling salesman person problem. Practical part draws a comparison among efficiency of several methods solving this problem in environment of real world examples. In summary analysis are these methods evaluated and consequently chosen and implemented most effective method for company, which want to use it to determining most optimized tours for distributing goods.
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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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Use of savings algorithm in messenger problem
Gőtz, Ondřej ; Fábry, Jan (advisor) ; Kobzareva, Maria (referee)
The diploma thesis deals with the use of heuristic methods for solving messenger problems. The first part focuses on the proposed vehicle routing problems, especially on travelling salesman problems and the messenger problems. For individual problems are theoretically discussed mathematical models for variants with one or more vehicles and the expansion of the use of time windows and capacity constraints. The second part introduces heuristic algorithms for the method of nearest neighbour, savings method, insertion method and the exchange method on the travelling salesman problems. Then all of the mentioned algorithms are modified for use in three variants of messenger problem. First, the disposition of one vehicle, the second allows more messengers in the same starting point and the last option is more messengers at different starting points. The last part describes computational experiments and comparison of results provided by different methods. The diploma thesis includes application for solving messenger problems using savings methods programmed in Visual Basic for Application in MS Excel.
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Parcel pick-up optimization
Kozárová, Barbora ; Skočdopolová, Veronika (advisor) ; Šindelářová, Irena (referee)
Vehicle routing problems solve problems of optimizing the transport routes. The principle of solutions of problems of the first type is finding the shortest circuit that begins and ends in the same place and includes places that can be visited in any order, each of them has to be visited exactly once. In the second type of problems there is also considered the size of the requirements and the capacity of the vehicle, which has to return back to the store. Both tasks can be extended to the so-called time windows, which indicate the interval between the earliest possible and latest allowable start of the customer service. This work aims to calculate the optimal route for the drivers of unnamed wholesale company. The objective is to minimize the distance travelled per day in order to reduce fuel costs. The solution is implemented using the models of Travelling Salesman problem, Vehicle Routing problem and their modifications with time windows through systems LINGO, eventually GUROBI, and MPL for Windows. To illustrate the application of heuristic methods the calculation is carried out by savings method.
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Optimization distribution and collection of infusion solutions
Kravciv, Zbyněk ; Fábry, Jan (advisor) ; Pelikán, Jan (referee)
There are many distribution tasks, that vary in a number of vehicles, time windows, dividend or undivided delivery or if it is static problems or dynamic problems. In this essay I focus just on few of them. At first I put my mind to simple statistic distribution task with one vehicle. Later I extend it with time windows, when the point can be served by one car and by many cars. In the essay it will be solved the real task of distribution and delivery transportation of infusion in the hospitals. Because of the difficulty of solution I have to use the heuristic methods - Method of nearest neighbour, Savings method and Insert method. All these methods are modified by capacity requirements, time windows and also observence of the rules, which the drivers have to keep during a distribution. The aim is to minimize the distance travelled by the vehicles. And at least the company could be recommended the best solution.
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