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Training plan solved by assignment problem
Vejvodová, Tereza ; Borovička, Adam (advisor) ; Fábry, Jan (referee)
The aim of the bachelor thesis is to create the best training plan for the dancers on a weekly training camp. This is the assignment of categories to certain hours of training for every day on training camp. Each category has different requirements in terms of days of training and of course hours of individual trainings. This problem solves an assignment problem and for calculation is used optimization program LINGO. The most effective plan for dancers will be found with this program. This plan should be fair and should satisfy all categories. In the theoretical part is described linear programming, primarily assignment problem and integer programming. In the practical part is the theory applied in practice and it is created schedule of categories for each day of training camp.
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Optimization of logistics and business processes in Bookretail s.r.o.
Hollayová, Nela ; Zouhar, Jan (advisor) ; Kuncová, Martina (referee)
The subject of the thesis is the optimization of one the key processes in a book company, namely warehouse logistics. This problem consist of two parts; first part focuses on route optimization of completion of customers' orders on daily basis, second part focuses on assigning of storage subsystems and their interconnection. The proposed solution uses a traveller salesman problem implemented into intranet application. Second problem was designed as quadratic assignment problem with use of ex post data analysis. On the basis of achieved results, we presented effective procedures for solving both of aforementioned problems and suggested their implementation into the company's enterprise resource planning system. Keywords:
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Use of simulation model for the estimates of auction house’s revenues
Ondráčková, Kristýna ; Kuncová, Martina (advisor) ; Borovička, Adam (referee)
The auction is a form of trading, which is becoming more popular in recent years. For English auction the typical object intended for trading is art or antique etc. Auction houses require the most accurate estimates of total sales for each auction because of their economic activity. These estimates are constructed, but the only information that is available is starting price of auctioned objects (paintings). Two methods have been proposed for purpose of this estimation. They are conducted in the application Crystal Ball. Selling prices of the objects are generated in the first method and total sales are estimated with the help of application assignment problem. The second method consists in the simple sum of generated selling prices. The cornerstone of these methods is the distribution from which a coefficient is generated that sets increase of the starting prices to selling prices. The first part of practical application is dedicated to estimating parameters of this distribution. In the second part, total revenues are estimated using both methods. In conclusion there is the assessment of the suitability for both methods and estimated distributions. Method that provides the most accurate estimate of total sales for auction house is determined there also.
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Optimalization of labor force in a Family Hotel
Balšánková, Tereza ; Skočdopolová, Veronika (advisor) ; Šindelářová, Irena (referee)
Primary objective of this bachelor thesis "Optimalization of laber force in a Family Hotel" is to solve the linear task of optimalization of the work force in the family hotel Balkan utilizing the Hungarian method and sub-sequently using the optimalization system LINGO. For optimalization is used the modification of assignment problem, which belongs to typical tasks of linear programing, so called distribution task. Theoretical part of this thesis describes not only linear programming itself, yet it is just focused to distrubution methods. In the practical part the task is treated by both of the above mentioned ways. The objective is to create the schedule of assignments of the given position to the concrete person at certain day. The secondary objective of the bachelor thesis is to compare the results of the solution of both methods and evaluate which variant is more suitable in this case.
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Logical puzzles and brainteasers as optimization problems
Lukesová, Kristýna ; Chýna, Vladislav (advisor) ; Šindelářová, Irena (referee)
This thesis applies classical optimization problems such as assignment or set-covering problem on logical puzzles or brainteasers. Listed in the first part are mathematical model, description and typical example of each optimization problem used in this thesis. The second part contains these models applied to the particular brainteasers for example Sudoku or Einstein's Puzzle. Exercises are divided into simpler and more complex ones. There is specification, source and a described method of solution stated for each of them. The calculation examples use Lingo or MS Excel or both. The aim is to show the possibility to address logical puzzles and brainteasers with the use of optimization problems, and thus confirm the wide possibilities of using these models. These examples can clarify and diversify the curriculum.
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Graph theory – an alternative method of solving LP problems
Hrabovská, Michaela ; Šindelářová, Irena (advisor) ; Chýna, Vladislav (referee)
This bachelor thesis analyses an example of an alternative method of solving selected linear programming problems using graph theory. These alternative methods are explained not only theoretically, but also illustrated on the practical examples. For comparison, there is a theoretical description and also practical solution of selected problems with using linear programming stated in the text. In the introductory part of the thesis, the theory of operations research is briefly discussed. The selected problems are: knapsack problem, transportation problem, assignment problem.
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Staff scheduling in health services
Uhlíř, Filip ; Dlouhý, Martin (advisor) ; Fábry, Jan (referee)
Purpose of this thesis is to show different solutions for the staff scheduling in health services. There will be shown various issues that this special assignment problem brings. The text will describe solutions using mathematical modeling and one solution using heuristics. Solutions of the mathematical models are divided into two parts. The first part describes two models that address the assignment problem for night duties only. The second part describes two more models that address the assignment problem for the whole day. The models are compared with each other. Among other things, there are also described several possibilities how different models could be combined. Model example is calculated for the staff allocation on night duties. The example uses some of the conditions from the two models that solve this assignment problem.
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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, container-transportation 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 end-user's pages, is described. By this tool the end-user 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 end-pages of selected distribution problems and the list of solvers supported by AIMMS.
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The Solving of Distribution Problems in MS Excel / LINGO
Bisová, Sára ; Jablonský, Josef (advisor) ; Skočdopolová, Veronika (referee)
The goal of this work is to explain the topic of distribution problems, special kind of linear programming problems, and also to show possibilities for solving them in some programming systems. For solving several types of distribution problems - transportation problem, container transportation problem, assignment problem, allocation problem and travelling salesman problem - I have created an application which connects MS Excel with programming language LINGO. This connection is realized by means of VBA - Visual Basic for Applications. There are described the main procedures and functions of LINGO and VBA including minute description of interconnection of these systems. Created application is illustrated on several small problems in the last part of work.
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Assignment problem
Partynglová, Soňa ; Lagová, Milada (advisor) ; Kalčevová, Jana (referee)
This thesis is describing one of the most popular method (Hungarian method) for solving the assignment problem. This type of problem is usually just defined by most the writers instead of it's real treatement. The main target of this thesis was to resume the knowledge of this problem, to define it carefully and to use Hungarian method for finding the best solution. This thesis also shows the differences between solving this problem by minimalisation or maximalization of the function of effectiveness and this thesis also shows how to solve the unbalanced tasks.
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