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undergraduate thesis
Simpleks metoda
2024. urn:nbn:hr:190:644160
Jajac, Luka
University of Rijeka
Faculty of Engineering
Department of Mathematics, Physics, and Foreign Languages
Section of Applied Mathematics

Cite this document

Jajac, L. (2024). Simpleks metoda (Undergraduate thesis). Rijeka: University of Rijeka, Faculty of Engineering. Retrieved from https://urn.nsk.hr/urn:nbn:hr:190:644160

Jajac, Luka. "Simpleks metoda." Undergraduate thesis, University of Rijeka, Faculty of Engineering, 2024. https://urn.nsk.hr/urn:nbn:hr:190:644160

Jajac, Luka. "Simpleks metoda." Undergraduate thesis, University of Rijeka, Faculty of Engineering, 2024. https://urn.nsk.hr/urn:nbn:hr:190:644160

Jajac, L. (2024). 'Simpleks metoda', Undergraduate thesis, University of Rijeka, Faculty of Engineering, accessed 05 April 2025, https://urn.nsk.hr/urn:nbn:hr:190:644160

Jajac L. Simpleks metoda [Undergraduate thesis]. Rijeka: University of Rijeka, Faculty of Engineering; 2024 [cited 2025 April 05] Available at: https://urn.nsk.hr/urn:nbn:hr:190:644160

L. Jajac, "Simpleks metoda", Undergraduate thesis, University of Rijeka, Faculty of Engineering, Rijeka, 2024. Available at: https://urn.nsk.hr/urn:nbn:hr:190:644160

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Metadata
TitleSimpleks metoda
Title (english)Simplex method
AuthorLuka Jajac
MentorIvan Dražić (mentor)
Committee memberDubravko Franković (predsjednik povjerenstva)
Committee memberIvan Dražić (član povjerenstva)
GranterUniversity of Rijeka
Faculty of Engineering
(Department of Mathematics, Physics, and Foreign Languages)
(Section of Applied Mathematics)
Rijeka
Defense date and country2024-09-10, Croatia
Scientific / art field,
discipline and subdiscipline		TECHNICAL SCIENCES
Electrical Engineering
Abstract
Ovaj rad predstavlja analizu simpleks metode, temeljnog algoritma u domeni linearng programiranja. U uvodnom dijelu rada, istražuje se povijesni razvoj simpleks metode, naglašavajući njen značaj i doprinos evoluciji ove matematičke discipline. Slijedi detaljno objašnjenje matematičkog okvira problema linearne optimizacije, uključujući definicije funkcija cilja, ograničenja i strukture samog linearnog programa. Poseban fokus stavljen je na koncept konveksnosti i njegovu ključnu ulogu u... More primjeni simpleks metode. Definiraju se konveksni skupovi i konveksne funkcije, te se matematički dokazuje konveksnost linearnih funkcija. Rad postupno otkriva mehanizme simpleks metode, krećući se od grafičke metode, preko ključnih elemenata poput simpleks tablice i tehnike pivotiranja, do rješavanja problema minimizacije. Osim osnovnih principa, obrađuju se i napredne teme poput Charnesove M metode, koja proširuje primjenu simpleks metode na probleme s početnom nedozvoljenom točkom, te analize osjetljivosti, koja omogućuje evaluaciju utjecaja promjena ulaznih parametara na optimalno rješenje. Konačno, praktična primjena simpleks metode ilustrirana je kroz primjenu na konkretnom inženjerskom problemu, pri čemu je rješavanje provedeno korištenjem Excel Solver-a. Less
Abstract (english)
This work presents analysis of the simplex method, a fundamental algorithm in the field of linear programming. The introductory part delves into the historical development of the simplex method, emphasizing its significance and contribution to the evolution of this mathematical discipline. A detailed explanation of the mathematical framework of linear optimization problems follows, including definitions of objective functions, constraints, and the structure of linear programs... More themselves. Particular attention is given to the concept of convexity and its crucial role in the application of the simplex method. Convex sets and convex functions are defined, and the convexity of linear functions is mathematically proven. The work gradually unveils the mechanisms of the simplex method, starting from the graphical method, moving through key elements like the simplex tableau and the pivoting technique, and arriving at the solution of minimization problems. Beyond the basic principles, advanced topics are addressed, such as the Charnes M method, which extends the application of the simplex method to problems with an infeasible initial solution, and sensitivity analysis, which allows for the evaluation of the impact of changes in input parameters on the optimal solution. Finally, the practical relevance of the simplex method is illustrated through its application to a concrete engineering problem, where the solution is obtained using Excel Solver. Less
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:190:644160
Study programmeTitle: Undergraduate University Study of Electrical Engineering
Study programme type: university
Study level: undergraduate
Academic / professional title: sveučilišni/a prvostupnik/prvostupnica (baccalaureus/baccalaurea) inženjer/inženjerka elektrotehnike (sveučilišni/a prvostupnik/prvostupnica (baccalaureus/baccalaurea) inženjer/inženjerka elektrotehnike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence Attribution 4.0 International (CC BY 4.0) icon
Created on2024-09-10 10:52:22
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