|
|
Postoptimization analysis in parametric programming
Ten, Anastassiya ; Sekničková, Jana (advisor) ; Skočdopolová, Veronika (referee)
This bachelor thesis deals with postoptimality analysis of parametric programming problems. Parametric programming problem is problem, where some of the coefficients are not constant but depend on one or several parameters. Postoptimality analysis explores intervals of stability of coefficients in an initial solution and impact of additional changes in the assignment of the problem. Mentioned theory explains main terms and methods, which were illustrated on practical examples.
|
|
|
The choir’s tour planning - an application of travelling salesman problem
Marešová, Iva ; Skočdopolová, Veronika (advisor) ; Šindelářová, Irena (referee)
This thesis deals with planning a journey for a choir's tour by means of different methods of mathematical modelling. The first approach is the application of a travelling salesman problem. The study aims to find the shortest closed cycle which will give us an optimal solution. In the case which is solved in this thesis the model of the travelling salesman problem is partly modified because our goal is to choose only half of all the places which are the most effective for us. The thesis focuses on the application of those methods which give us only an approximate solution, particularly the method of the nearest neighbour and the method of change replacement. The first part of the thesis is devoted to the theory dealing with linear programming, distribution problems, heuristic methods and computer programmes for optimization. In the next part the discussed methods are applied to the concrete case in which the journey for the tour is planned. At the end of this thesis there are mentioned modifications which could be solved in this type of problems.
|
|
|
Multiple Criteria Decision Making of Stocks Traded on BCPP in Context of Financial Crisis.
Protiva, Vít ; Kuncová, Martina (advisor) ; Skočdopolová, Veronika (referee)
The subject of the diploma paper is Multiple Criteria Decision Making of Stocks Traded on Prague Stock Exchange during financial crisis in the years 2008 and 2009. Diploma paper is divided into two sections. First section mainly focus on introduction of multiple criteria decision algorithms and fields, where are algorithms applied. Main purpose of second part of the diploma paper is to compile classified semence of stocks based on fundamental investment principals and make comparison of various orders based on both years and each algorithms.
|
|
|
Alternative rules for determining pivot columns and pivot rows in the simplex method
Leontiev, Andrey ; Kalčevová, Jana (advisor) ; Skočdopolová, Veronika (referee)
In my thesis I tried to describe the problems of choice of a pivot in the simplex method. The first part is devoted to the mathematical model of linear programming and simplex method in general. Here are explained the key concepts and principles of this method. There is the description of alternative rules for choosing a pivot using the simplex method in the second part. The description of each method is supported by example. I emphasize here the proofs of finite algorithm for each rule. In the last part of my thesis I have placed my own examples to show the different effects using different methods.
|
|
|
Application of the blending problem into the marketing campaign making
Záhorovský, Radek ; Skočdopolová, Veronika (advisor) ; Šindelářová, Irena (referee)
Application of the blending problem is one of the basic tools used in the marketing campaign making. It uses the theoretical knowledge of the linear programming in the real-world problem. This method is used for the optimization of required goals accepting the given budget and conditions. Linear programming is one of the tools suitable for maximizing the efficiency of the spent costs when scheduling the budget into the different media types. Media agencies normally use sophisticated software based on the linear programming methods. The results can be implemented into other specific situations and for other companies with the same kind of product. After that results can be analyzed for the future use. Basic problem of application of the blending problem is the fact that it is difficult to include all the factors affecting the impact of marketing campaign into the mathematical model.
|
|
|
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.
|
|
|
Nutrition problem usage for horse feed ration production
Králová, Eliška ; Skočdopolová, Veronika (advisor) ; Šindelářová, Irena (referee)
Concern of this bachelor's thesis is to optimize the contents of the daily feed ration for horses, which must meet their nutritional requirements. The first chapter is devoted to the theory of decision problems using linear programming. In the list of typical linear problems there is a closer specification of the nutritional problem, description of its use and a brief mention of its history. Next part deals with horse nutrition, which includes the requirements of the nutrient content of daily ration and the information about basic feed. Then the practical assignment is defined, which is essential for formulating economical and mathematical model, solved using Solver tool in Microsoft Excel. After interpreting the results, the model is extended with new constraints and recalculated. Outcome of this work is the optimal solution for two models that meet the intended objective -- to help the breeder with creating a nutritionally balanced feed ration for horses and minimizing the costs.
|
|
|
Application of set-covering problem to fire district station Ovčáry
Ulrychová, Lenka ; Skočdopolová, Veronika (advisor) ; Kuncová, Martina (referee)
This thesis deals with the set-covering problem which belongs to distribution problems of the linear programming and in a practice can be found in many forms. The main goal of the standard set-covering problem is the construction of a new operating station which contains a degree of danger, but this thesis is focused on one operating station and examines the decision about its construction like a station of type JPO I, the problem contains so-called degrees of danger. Thesis is based on the real data provided by Fire Brigade of the Central region (Hasičský záchranný sbor Středočeského kraje). The theory of the distribution problems and optimization system MPL (which is the problem solved by) is presented in the first part. There a reader can also find a little information from the history of The Fire Brigade of the Czech Republic (HZS ČR). In the next part there is the description of modification for examining area coverage of the territory, where fire units are included instead of operating stations.
|
|
|
Optimization of Business Trips Schedule -Vehicle Routing Problem Application
Dvořáčková, Tereza ; Šindelářová, Irena (advisor) ; Skočdopolová, Veronika (referee)
My bachelor thesis deals with the special linear programming problems, so called distribution problems. Special attention is paid to the travelling salesman problem (TSP) and the vehicle routing problem (VRP). The introductory theoretical chapters explain mathematical models of selected distribution problems, as well the description of some heuristic methods for solving the TSP problem. The modifications of these heuristics are then applied to the real vehicle routing problem. In that real task (included in the last part of this thesis) the daily schedule for a sales representative of one unnamed Czech company is optimized. That sales representative regularly attends customers in his assigned territory and my optimization is focused on saving his time. The results obtained by means of heuristics as well by LINGO software are compared in the thesis conclusion. In chapter 3.5 the real task was modified by means of introducing new limitations, so-called time windows. The results of my thesis will be present to the company.
|
|
|
University Schedule Optimisation
Skrbková, Tereza ; Jablonský, Josef (advisor) ; Skočdopolová, Veronika (referee)
Scheduling is a practical optimisiation problem which can be solved by means of integer or binary programming methods. This paper focuses on university scheduling, in particular the schedule of the University of Economics in Prague, it is however possible to apply the results to schedules of other universities. We begin with the basics of linear programming, focusing on integer and binary programming as well as selected methods used to solve these problems. We then construct an optimisation model for the schedule of a subset of subjects based on real requirements (data 2009) and we compare the results with the actual schedule of the University of Economics in Prague. In conclusion we discuss some of the assumptions made during model development. The model is then generalised to include the entire set of subjects of the university. For the conversion of the software results into a more legible format, we include two MS Excel macros as part of this paper.
|
guest ::
