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Combinatorial optimization problems in waste management
Michalová, Jitka ; Šeda, Miloš (referee) ; Kůdela, Jakub (advisor)
This master’s thesis is focused on creation of an optimization model for the location allocation problem. The first part of the thesis is an introduction to optimization, which describes the most common methods for solving optimization problems and contains a list of approaches and methods most commonly used in waste management. The next part deals with the creation of a binary integer programming problem, its application to real data and a comparison of MATLAB and ILOG CPLEX solvers. Lastly, hierarchical and kmeans clustering are introduced, they are then applied to specific largescale problems.
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Optimal path planning for electric vehicles
Horák, Filip ; Šoustek, Petr (referee) ; Kůdela, Jakub (advisor)
This master’s thesis is about optimal route planning for electric vehicles. The first, theoretical part of this work introduces the issue and describes several heuristic methods that have been used to address optimization tasks. A practical part of the thesis is based around software implementation of the methods described earlier. Finally, several experiments and comparisons of obtained results are carried out.
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Applications of scheduling algorithms in railway transportation
Fajmon, Michal ; Kokrda, Lukáš (referee) ; Pavlas, Martin (advisor)
Bachelor’s thesis is focused on creation of mathematical model, which uses multiple methodsforwastecollectionatthelevelofmunicipalities.Modelisfocusedon railfreight transport. Main reasons are of lower production of emissions and reduction of burden on road traffic. In order to create model, the knowledge of graph theory, integer and linear programmingisused.CreatedmodelisimplementedinGAMSenvironmentonsmallscale data. At the end there are stated possibilities for further development of the model.
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The Facility Location Problem for an Alternative Delivery Service
Vaněk, Petr ; Červinka, Michal (advisor) ; Habibi, Arash (referee)
The main intention of the bachelor thesis is to introduce all necessary theory to under- stand and apply the facility location problem for an alternative delivery service. Solving the facility location problem we are able to find optimal warehouse locations to minimize transportation costs from a firm to customers. Our attention is focused on an alternative delivery service which is slowly becoming to be taken seriously in logistic disciplines be- cause many companies are trying to apply drones or robots for shipping goods. The first part of this thesis deals with an important theoretical background needed to understand the facility location problem. Microeconomic view of the problem is presented, basic knowledge of mathematical programming with algorithms is explained and the facility location problem itself is defined. Moreover, each step of the branch & bound algorithm for the facility location problem is explained on an example from Prague. In the practical part of the thesis, we solve a real problem for the Czech company which would like to im- plement a drone delivery service in Prague. Finally, we discuss future technical progress and its impacts on autonomous delivery service, legislative and privacy problems with a drone delivery system in Prague and other possible usage of autonomous vehicles in...
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Assignment problem with application to heath service
Tlapák, Martin ; Kopa, Miloš (advisor) ; Lachout, Petr (referee)
This bachelor's thesis deals with the theory of the nurse scheduling problem using the theory of integer programming. That is why we define basic concepts and present basic theorem of integer programming. We present the algorithm made for solving integer programming. Next we define a basic concept of as- sigment problem. We show how to solve assigment problem by the Hungarian method. Finally we solve the real nurse scheduling problem. The nurse's pref- erences are included in our model. We are finding solution which is suitable for the labour code of the Czech Republic and the special requests of the stressful workplace. 1
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A knapsack problem
Piskačová, Nikola ; Kopa, Miloš (advisor) ; Lachout, Petr (referee)
This work deals with the theory of integer programming. In the first part, there are defined the basic concepts and there are mentioned the two most used methods for solving integer problems. Namely, it is the Branch and Bound method and the Cutting Plane method. In the second chapter, there is described the Knapsack Problem and its various formulations. This problem is a special case of integer optimalization. Next, there is a practical part, where a real problem is solved. The problem is how to place the products in shelves in equipment in the most effectively way. In this chapter is described how to process input data, create a model and solve the problem. In the second part of the practical part, the basics of stochastic optimalization and solution of these problems by the Scenario method are presented. This method is used to solve the previously mentioned problem if the delivery days are random. The aim of this work is to show the applicability of formulations of Knapsack Problem and to compare the obtained results. 1
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Scheduling optimization problems in education
Puček, Samuel ; Kopa, Miloš (advisor) ; Branda, Martin (referee)
This work deals with the theory of integer programming. After defining the ba- sic concepts, it presents two algorithms suitable for solving integer problems. Firstly, it talks about the branch and bound algorithm and secondly, it talks about the cutting plane algorithm. Next, it presents an assignment problem, which is a special case of integer programming. The work describes the hungarian method and explains its usage on exemplary examples. The last part of the work solves the real problem from the practice. The aim of this section is to find an optimal schedule for classes one to seven of the selected elementary school. It introduces input data processing, creating a model and the solution. Obtained results are accompanied by a brief discussion. 1
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Analysis of the performance growth of the optimization solvers
Škvarková, Alexandra ; Jablonský, Josef (advisor) ; Fábry, Jan (referee)
It would not be possible to solve real optimization problems, which usually contain a huge number of variables and constraints, without high-performance optimization systems. Today's software market offers a vast number of different systems available to provide solutions to linear and non-linear optimization tasks, including integer conditions. One such optimization system is called Gurobi. It is available in several versions. This thesis is focused on the performance comparison of three solver versions (i.e. 7.0.2, 6.0.5 and 5.0.2) using tasks that are in the MPS format, they are obtained from the MIPLIB 2010 electronic library, namely from the Benchmark section. The results are compared according to the time period needed to solve the task for each investigated version.
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Vertex coloring algorithms in scheduling problems under uncertainty
Hájek, Štěpán ; Branda, Martin (advisor) ; Lavička, Karel (referee)
This thesis concerns solutions to problems that arise in optimizing fixed interval scheduling under situations of uncertainty such as when there are random delays in job process times. These problems can be solved by using a vertex coloring with random edges and problems can be formulated using integer linear, quadratic and stochastic programming. In this thesis is propo- sed a new integer linear formulation. Under certain conditions there is proved its equivalence with stochastic formulation, where is maximized the schedule reliability. Moreover, we modified the proposed formulation to obtain bet- ter corresponding to real life situations. In a numerical study we compared computational time of individual formulations. It turns out that the propo- sed formulation is able to solve scheduling problems considerably faster than other formulations. 1
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Particular Problems Related to the Vehicle Routing Problem
Kuklis, Imrich ; Pergel, Martin (advisor) ; Majerech, Vladan (referee)
Title: Particular Problems Related to the Vehicle Routing problem Author: Imrich Kuklis Department: Department of Software and Computer Science Education Supervisor: RNDr. Martin Pergel, Ph.D., Department of Software and Computer Science Education Abstract: In this thesis we present and implement some scheduling algorithms. In the first part we discuss the vehicle routing problem and its variants. In the second part we describe the algorihms we used in the thesis. In the third part we compare the algorithm by their results on several tests. In the last chapter we describe the documentation of the programs which we implemented and discuss the possible future extension of the thesis. Powered by TCPDF (www.tcpdf.org)
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