Title Metode za rješavanje linearnog programiranja te njihova primjena u ekonomiji : Završni rad Title (english) Methods for solving linear programming and their application in economics : Final paper Author Vanja Blagojević Mentor Martina Briš (mentor)Committee member Josipa Forjan (predsjednik povjerenstva)Committee member Martina Briš (član povjerenstva)Committee member Jasna Horvat (član povjerenstva)Granter Josip Juraj Strossmayer University of Osijek Defense date and country 2024-09-24, Croatia Scientific / art field, SOCIAL SCIENCES Abstract Linearno programiranje je osnova kvantitativnih metoda koje služe za optimizaciju resursa u
okviru određenih ograničenja, omogućavajući učinkovito donošenje poslovnih odluka. Glavni
cilj linearnog programiranja je maksimizirati profit ili minimizirati troškove koristeći
matematičke alate i metode za rješavanje problema. Rad je strukturiran u nekoliko dijelova koji
se bave teorijskim i praktičnim aspektima ove tehnike. U teorijskom dijelu, autor opisuje pojam
linearnog programiranja, njegov
... More povijesni razvoj i ključne pojmove. Pritom se osvrće na važne
etape u razvoju linearnog programiranja, počevši od modela Wassilyja Leontiefa i Leonida
Kantorovicha, pa sve do simpleks metode koju je 1947. godine razvio George Dantzig. U
praktičnom dijelu rada, fokus je na dvije glavne metode za rješavanje problema: simpleks
metoda i grafička metoda. Simpleks metoda, kao jedna od ključnih tehnika za rješavanje
složenih problema, ističe se po svojoj učinkovitosti u radu s mnogim varijablama i
ograničenjima. Ova metoda koristi iterativni proces za pronalazak optimalnog rješenja unutar
definiranih ograničenja. U radu su prikazani primjeri primjene ove metode kroz softverske alate
poput Microsoft Excela i dodatka Solver, gdje je poseban naglasak na rješavanju problema
transporta kako bi se minimizirali troškovi distribucije između različitih lokacija. Grafička
metoda, iako jednostavnija, koristi se za vizualno rješavanje problema s najviše dvije varijable.
Unatoč ograničenjima u složenijim problemima, ova metoda pruža koristan okvir za
razumijevanje osnovnih principa optimizacije. U radu je detaljno prikazan primjer primjene
grafičke metode u Excelu, gdje se rješava problem optimizacije proizvodnje s ciljem
maksimizacije profita. Prema autoru, linearno programiranje ima široku primjenu u ekonomiji.
Primjeri uključuju optimizaciju proizvodnje, smanjenje troškova transporta, upravljanje
zalihama, financijsko planiranje i raspodjelu radne snage. Autor također donosi primjere iz
stvarnog svijeta, poput optimizacije ulaganja u hedge fondovima (primjer Bridgewater
Associates), upravljanja rafinerijskim procesima u naftnim kompanijama (primjer Royal Dutch
Shell) te optimizacije opskrbnog lanca u maloprodaji (primjer Walmart). Zaključno, rad
naglašava važnost linearnog programiranja u rješavanju složenih poslovnih i ekonomskih
problema. Simpleks metoda se pokazala kao najefikasnija za rad s velikim brojem varijabli, dok
grafička metoda ostaje korisna za jednostavnije, edukativne primjere. Linearno programiranje,
kao alat matematičke optimizacije, omogućava menadžerima i ekonomistima donošenje
informiranih odluka na temelju analize kvantitativnih podataka, čime se povećava učinkovitost
i profitabilnost. Daljnji napredak tehnologije dodatno će proširiti primjenu ovih metoda, čineći
ih još značajnijim u budućim gospodarskim okruženjima. Ovaj rad doprinosi boljem
razumijevanju značaja optimizacijskih metoda u poslovnom odlučivanju te ističe ključnu ulogu
linearnog programiranja u praktičnim rješenjima ekonomskih problema. Less Abstract (english) Linear programming is the basis of quantitative methods that serve to optimize resources within
certain constraints, enabling effective business decision-making. The main goal of linear
programming is to maximize profits or minimize costs by using mathematical tools and
methods to solve problems. The paper is structured in several parts dealing with the theoretical
and practical aspects of this technique. In the theoretical part, the author describes the concept
of linear programming, its
... More historical development and key terms. In doing so, he looks back at
the important stages in the development of linear programming, starting with the model of
Wassily Leontief and Leonid Kantorovich, all the way to the simplex method developed in 1947
by George Dantzig. In the practical part of the paper, the focus is on two main methods of
problem solving: the simplex method and the graphical method. The simplex method, as one of
the key techniques for solving complex problems, stands out for its efficiency in working with
many variables and constraints. This method uses an iterative process to find the optimal
solution within defined constraints. The paper presents examples of the application of this
method through software tools such as Microsoft Excel and the Solver plugin, where special
emphasis is placed on solving transportation problems in order to minimize distribution costs
between different locations. The graphical method, although simpler, is used to visually solve
problems with a maximum of two variables. Despite its limitations in more complex problems,
this method provides a useful framework for understanding the basic principles of optimization.
The paper presents in detail an example of the application of the graphical method in Excel,
where the problem of optimizing production with the aim of maximizing profit is solved.
According to the author, linear programming is widely used in economics. Examples include
production optimization, transportation cost reduction, inventory management, financial
planning, and labor allocation. The author also provides examples from the real world, such as
optimizing investments in hedge funds (example Bridgewater Associates), managing refinery
processes in oil companies (example Royal Dutch Shell) and optimizing the supply chain in
retail (example Walmart). In conclusion, the paper emphasizes the importance of linear
programming in solving complex business and economic problems. The simplex method
proved to be the most efficient for working with a large number of variables, while the graphical
method remains useful for simpler, educational examples. Linear programming, as a
mathematical optimization tool, enables managers and economists to make informed decisions
based on quantitative data analysis, thereby increasing efficiency and profitability. Further
advances in technology will further expand the application of these methods, making them
evenmore significant in future economic environments. This paper contributes to a better
understanding of the importance of optimization methods in business decision-making and
highlights the key role of linear programming in practical solutions to economic problems. Less Keywords
linearno programiranje
kvantitativne metode za poslovno odlučivanje
grafička metoda
simpleks metoda
maksimizacija
minimizacija
optimizacija
Keywords (english)
linear programming
quantitative methods for business decision-making
graphical method
simplex method
maximization
minimization
optimization
Language croatian URN:NBN urn:nbn:hr:145:994793 Study programme Title: ECONOMICS AND BUSINESS ECONOMICS - UNDERGRADUATE - UNIVERSITY Type of resource Text File origin Born digital Access conditions Open access Terms of use Created on 2024-12-11 10:45:08
