Cjelobrojno programiranje

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.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