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master's thesis
Cjelobrojno programiranje
Zagreb: University of Zagreb, Faculty of Science, 2015. urn:nbn:hr:217:468496
Čulina, Tina
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Čulina, T. (2015). Cjelobrojno programiranje (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:468496

Čulina, Tina. "Cjelobrojno programiranje." Master's thesis, University of Zagreb, Faculty of Science, 2015. https://urn.nsk.hr/urn:nbn:hr:217:468496

Čulina, Tina. "Cjelobrojno programiranje." Master's thesis, University of Zagreb, Faculty of Science, 2015. https://urn.nsk.hr/urn:nbn:hr:217:468496

Čulina, T. (2015). 'Cjelobrojno programiranje', Master's thesis, University of Zagreb, Faculty of Science, accessed 03 November 2024, https://urn.nsk.hr/urn:nbn:hr:217:468496

Čulina T. Cjelobrojno programiranje [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2015 [cited 2024 November 03] Available at: https://urn.nsk.hr/urn:nbn:hr:217:468496

T. Čulina, "Cjelobrojno programiranje", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2015. Available at: https://urn.nsk.hr/urn:nbn:hr:217:468496

Metadata
TitleCjelobrojno programiranje
AuthorTina Čulina
MentorMarko Vrdoljak (mentor)
Committee memberMarko Vrdoljak (predsjednik povjerenstva)
Committee memberMladen Vuković (član povjerenstva)
Committee memberTina Bosner (član povjerenstva)
Committee memberNikola Sarapa (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2015-11-26, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
Cjelobrojno linearno programiranje se bavi problemom optimizacije linearnog funkcionala uz linearne uvjete tipa jednakosti i nejednakosti gdje je dodatno uveden zahtjev cjelobrojnosti na neke (ili sve) varijable. Područje primjene cjelobrojnog linearnog programiranja je široki : proizvodnja, transport i distribucija, marketing, financijsko ulaganje i planiranje, raspored zaposlenika… Najčešće metode pri rješavanju problema cjelobrojnog programiranja su metoda grananja i ograđivanja i metoda odsijecajućih ravnina. U ovom radu smo istražili metodu odsijecajućih ravnina. U prvom i drugom poglavlju smo se upoznali s teorijom potrebnom da bi se dokazao glavni teorem za metodu odsijecajućih ravnina, a to je da se u konačno mnogo koraka odsijecanjem poliedarskog skupa P može dobiti njegova cjelobrojna ljuska i pokazali smo ocjenu broja tih koraka. U trećem poglavlju smo uveli algoritam za metodu odsijecajućih ravnina te smo pokazali dva primjera problema cjelobrojnog linearnog programiranja riješenih metodom odsijecajućih ravnina.
Abstract (english)
Integer linear programming deals with the optimisation problem of linear functional, concerning linear constraints of equality and inequality, where some (or all) variables are additionally restricted to be integer. Scope of integer linear programming usage is wide: production, transport and distribution, marketing, financial and investment planning, employees scheduling etc. The most common methods for solving integer programming problems are branch and bound method and cutting plane method. In this paper we studied the cutting plane method. In the first two chapters we’ve met the theory necessary to prove the main cutting plane method theorem, which says that the integer hull of polyhedral set P can be obtained by cutting its parts in finite number of times. Furthermore, we showed the rating of this finite steps numbers. In the third chapter, we’ve introduced the algorithm of cutting plane method and demonstrated two integer linear programming problem examples, solved with cutting plane method.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:468496
Study programmeTitle: Finance and Business Mathematics
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2019-01-08 11:10:41