
Capacitated Arc Routing Problem
Franc, Zdeněk ; Pelikán, Jan (advisor) ; Fesenko, Anastasiya (referee)
The Capacitated Arc Routing Problem has many applications in real life. The aim of this problem is to minimize the total cost at fulfilment of the requirements of arcs. The Capacitated Arc Routing Problem is an extension of the Chinese Postman Problem, which is a special type of the Vehicle Routing Problems. In this thesis is explained the issue of the Chinese Postman Problem and its extensions at first. Subsequently the applications of mathematical models are illustrated on a model example. However these mathematical models, which are searching the optimal solution, do not use so much in reality. Therefore the randomized heuristic algorithm for solving these problems is suggested and programmed in this thesis. Subsequently this heuristic was applied to case study of garbage collection in Podebrady city.


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 NPhard 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.


The real use of operations research methods in conjunction with logistics technologies
Fesenko, Anastasiya ; Kuncová, Martina (advisor) ; Pelikán, Jan (referee)
This diploma focuses on the real use of operations research methods in conjunction with logistics technologies. The aim is to show the way of optimization and simulation methods application and to evaluate if these methods are suitable tools for logistics technology application. Following logistic technologies were analysed: Just in Time, Kanban, CrossDocking and Hub and Spoke. Used mathematical tools include: mixed linear programming models, distribution models, methods of multicriteria evaluation and simulation models. On the basis of mathematical models 4 examples of new technologies introduction or analysis of already functioning systems have been solved.


Optimal composition of groceries for mountain trip
Fesenko, Anastasiya ; Kalčevová, Jana (advisor) ; Flusserová, Lenka (referee)
This work is aimed towards the application of knapsack problem in practical example of packing of groceries for mountain trip. The knapsack problem is one of the tasks of integral programming; those are the models that can only variably accept the integral value. The solutions of integral tasks are usually very meticulous. That is why for their solution special algorithms were created, which are capable of discovering an integral solution of such tasks, for example, branch and bound method, Balas method etc. These types of algorithms are defined in the first part of this work. While writing this thesis a considerable emphasis was put into application of its result in practice. Hence, for achieving applicability practical tasks are solved from various angles and therefore various aims have been set forth in each solution option. The results of each option are interpreted and then the differences are explained.
