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Analysis of reduced and shadow prices in linear programming problems with lower and upper bounds
Průšová, Lucie ; Jablonský, Josef (advisor) ; Kořenář, Václav (referee)
Abstract Title: Analysis of reduced and shadow prices in linear programming problems with lower and upper bounds. Author: Lucie Průšová Department: Department of Econometrics Supervisor: doc. Ing. Milada Lagová, CSc. This thesis deals with linear programming problems with additional requirements that values of variables are greater or lower than a specified bound. Where applicable, the variable is limited on both sides. These values are called the upper and lower bounds. Lower bound can be a minimum required number of manufactured products and upper bound a maximum permissible quantity of a substance in the mixture. The thesis contain a formulation of original LP problems with lower and upper bounds which are solved by standard simplex method and by its modification for bounded variables. The aim of this study is to analyze and compare the reduced costs and shadow prices in the mentioned class of problems. At the end there will summarize the results of this work.
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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.
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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.
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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.
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Collection of Solved Linear Programming Problems
Ďuricová, Alexandra ; Šindelářová, Irena (advisor) ; Kořenář, Václav (referee)
The target of this bachelor thesis is to build new examples of linear programming. The examples in this work include all the formalities which are necessary for the correct interpretation. The entering tasks designed are based on real problems and consist of as much real values as possible. The work is divided into nine chapters and eight of them represent one area of linear programming. The first chapter is a short introduction into the theory of linear programming. The second chapter consists of two parts representing integer and non-integer programming. This chapter is the largest and contains 9 examples. The following four chapters consist of examples of non-integer programming and the last three chapters contain examples of integer programming.
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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.
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Support of management decision-making on transport networks
Přibyl, Vladimír ; Černý, Jan (advisor) ; Kavička, Antonín (referee) ; Peško, Štefan (referee)
The presented thesis is focused on a set of problems related to managerial decision-making concerning networks (particularly transportation networks), respectively - if we put it more precisely - the thesis focuses on the support of this decision-making by means of quantitative methods. A set of problems related to nets and decision-making concerning their individual parts or elements represents a very complex sphere which has been a subject of research for a number of decades. Out of this sphere, the thesis formulates and elaborates in great detail two problems, which - from the point of view of their practical significance - are important for the decision-making of managers of carriers, or the public sphere, and which have not been published in this form yet. The main point is the problem of how to find a subnet with a limited prolongation of routes between important pairs of vertices. Another problem is a design of a bus route in an area with a low demand. For each of these problems, the thesis offers an exact combinatorial solution method, furthermore a method based on integer linear programming, and - last but not least - also, of course, heuristic methods of solution. All these methods have been tested on a set of networks, which has been created for this purpose in a pseudo-random way in the frame of this thesis. The testing has been focused primarily on the comparison of the results provided by heuristic methods, which are of great importance - with regard to a great computational difficulty of exact methods - for feasible tasks on a larger scale. The tests have proved that the proposed heuristic methods are practically applicable and show results whicheven represent the optimal solution in a number of cases, or are only slightly distant from the optimal solution.
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The multiple knapsack problem
Černý, Vít ; Kalčevová, Jana (advisor) ; Suchánková, Tereza (referee)
The knapsack problem is one of the classical operations research problems. It belongs to the category of integer linear programming problems and is most often formulated as a binary problem. This thesis describes different categories of the problem and also some methods for finding their solution. Although there are precise algorithms for finding reliable optimal solution, some of the knapsack problems are so large that it would be impossible to follow the exact algorithms. Therefore, more complex knapsack problems belong to the complexity class of NP-complete. Yet there are a variety of heuristics and methods developed, which can lead to a sufficiently good solution in a relatively short time and relatively simple way. This paper focuses particularly on one of the problems described, the multiple knapsack problem. It is showed on a practical example how the problem can be solved.
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Use of simplex algorithm in planning the production
HRÁCHOVÁ, Iveta
The aim of this bachelor thesis is the arrangement of an optimal structure of vegetal and animal production by means of the simplex algorithm for linear programming; as well as the effective implementation of individual limitations of agricultural production into a simplex matrix resulting in the acquirement of a basic solution. The bachelor thesis upshot is a basis that provides maximization of the profit of a subject by given biologic, natural and economic regularities. By the basis we understand the structure of vegetal production together with the structure of livestock production.
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