
Application of Linear Programming on Project Management
Hrnčířová, Michala ; Zouhar, Jan (advisor) ; Fábry, Jan (referee)
There are two approaches to solving project management tasks. The first method is using specialized algorithms that do not always give optimal results. The second way is to use linear programming which includes designing mathematical models that are then solved by optimization systems. In my thesis I am dealing with three types of optimization tasks, two of which are basic linear programming tasks: basic project time scheduling and time scheduling of a project with variable action lengths. The focal point of the thesis is to assemble a mathematical model to solve the time scheduling of a project with limited resources. My goal is to design general mathematical models and to compare the results gained by the use of linear programming with those of specialized algorithms.


Using of AIMMS at solving of optimization models
Lacinová, Věra ; Jablonský, Josef (advisor) ; Zouhar, Jan (referee)
The bachelor's thesis is about AIMMS  a system for mathematical modeling. The aim of the thesis is to create a simple user's guide for interested individuals that want to use this system on the basic level. Practical part is about making models of selected distribution problems. Thesis is organized into three main chapters. The first chapter is about linear programming and selected distribution problems of linear programming. There is outlined development of linear programming and its place in mathematical modeling. In this chapter, mathematical models of selected distribution problems as transportation problem, containertransportation problem, allocation problem, covering problem and assignment problem are formulated. The second chapter is about AIMMS and describes how to work with this system. It contains basic information about the system and its author J. Bisschop. The next part informs how to work with system AIMMS. There is a way of declaration of individual sections and procedures in Model Explorer discussed. The AIMMS Page Manager, a tool for creating enduser's pages, is described. By this tool the enduser can change data sets and obtain results of analyzed problems. The third chapter is practical part. It contains the description of selected distribution problems with the emphasis on their implementation in AIMMS. Appendix contains endpages of selected distribution problems and the list of solvers supported by AIMMS.

 

Optimalization of flights and revisions on ČSA airplanes
Pourová, Alžběta ; Jablonský, Josef (advisor) ; Zouhar, Jan (referee)
Flights and revisions planning is the problem of assigning flights and revisions to aircrafts in such a way that constraints are satisfied, and some objective function is optimized. Objective function can be to minimalize the number of aircrafts. The intention of my thesis is to find the optimum solution in the problem of flights and revisions planning to aircrafts. In this work, I am using linear programming, which is important and irreplaceable in everyday practical use.


The Theory of Graphs and the Solution of Its Exercises in the System LINGO
Drechslerová, Tereza ; Jablonský, Josef (advisor) ; Zouhar, Jan (referee)
The aim of this bachelor thesis is to introduce basic types of exercises of theory of graphs and to display possible methods of their solution. I have chosen these types of exercises: finding minimal skeleton, finding maximum river and Critical Path Method (CPM) and I specify them. Praticular exercises are solved in the system LINGO and after that by specific algorithm for optimalization in the graph. Part of my work also presents explanation of basic terms and short historical review of developement of the theory of graphs.


Processing production in firm logistic
Altmanová, Lenka ; Fábry, Jan (advisor) ; Zouhar, Jan (referee)
The paper describes how logistic influence process in the firm, also there is a comparation with other firms in automobile section. And second part describes a case study of job scheduling in a mechanicalengineering production, the goal is to minimise the overall processing time. The production jobs are processed by machines. This problem is treated as a hybrid fivestage flowshop. In other words, the jobprocessing job consists of maximum five tasks, it depends on product, because there is 12 products, each has own production flow. It is a new type of flowshop in which the firststage scheduling depends upon the time scheduling of the second stage, and so on. A mathematical model and a heuristic method is formulated, The problem is the NP hardness. The case study is solved with the heuristic method and the solution achieved represents a 10% reduction of the processing time for the given set of jobs.


Optimalizace na železnici
Šárková, Hana ; Pelikán, Jan (advisor) ; Zouhar, Jan (referee)
Tato práce se zaměřuje na stanovení vhodného počtu vlakových jednotek různých typů na jedné lince. Je zde ukázán postup řešení založený na celočíselném modelu toku s více dodatečnými omezeními, vázanými na proces řazení vagonů ve stanicích.Tento přístup je aplikován na případovou studii z reálného života, která je založena na jízdním řádu NS Reizigers, což je hlavní Nizozemský provozovatel osobních vlaků.


Measuring of imperfect markets
Veselý, Mikuláš ; Dlouhý, Martin (advisor) ; Zouhar, Jan (referee)
Prologue: Introduction to the problem 1. chapter: Introduction of the microeconomic therms and characterisation of them 2. chapter: Ways of managing and measuring of market's imperfectness 3. chapter: Data aplication and calculation of indexes Final balance: estimation of outcomes


Sudoku  formulation of the problem and it 's solution
Novák, Jakub ; Jablonský, Josef (advisor) ; Zouhar, Jan (referee)
The purpose of this Bachelor thesis was to formulate sudoku problem and to create an application which was able to solve a real sudoku puzzles. First two chapters consist common information. First is about sudoku and second about linear programming. Third chaper is about formulation of the problem and it's mathematical model. In last chapter is written about creating of application which is separated into three parts. In first part there is enviroment of MS Excel which is going to be prepeared for inserting data and displaying of results. In second part is described created linear model in optimalization software MPL for Windows. The last part of creating of application contains object library OptiMax, which allows starting optimalization from MS Excel.


Ant Colony Optimization
Zahálka, Jaroslav ; Fábry, Jan (advisor) ; Zouhar, Jan (referee)
This diploma thesis deals with Ant Colony algorithms and their usage for solving Travelling Salesman Problems and Vehicle Routing Problems. These algorithms are metaheuristics offering new approach to solving NPhard problems. Work begins with a description of the forementioned tasks including ways to tackle them. Next chapter analyses Ant Colony metaheuristic and its possible usage and variations. The most important part of the thesis is practical and is represented by application Ant Colony Optimization Framework. It is easily extensible application written in Java that is able to solve introduced problems. In conclusion this work presents analysis of solutions on test data.
