A survey of applicability of Geometric programming methods for the purpose of solving of special class of nonlinear logistic problems

Abstract

Diplomsko delo prikazuje uporabnost metod geometrijskega programiranja (GP) za reševanje posebnega razreda nelinearnih logističnih problemov. Ti so v praksi zelo pogosti. Če vsebujejo posinomsko nelinearno kriterijsko funkcijo, se velikokrat izkaže uporaba GP metod kot najustreznejša za ugotavljanje optimalnih rešitev. V prvem delu so opisane GP metode za probleme brez omejitev in z omejitvami. Največji poudarek je namenjen pristopu z diferencialnim računom. Pri reševanju vsakega GP problema je potrebno postaviti ustrezno posinomsko kriterijsko funkcijo, ugotoviti morebitne omejitve in določiti stopnjo težavnosti reševanja problema. Probleme je v enostavnejših primerih možno reševati zgolj analitično, pri težjih pa je potrebno kombinirano reševanje, ki terja poleg analitičnih izračunov tudi numerične metode. V drugem delu so prikazani postopki reševanja hipotetičnih in realnih problemov s pomočjo GP metod. Kot je prikazano na primerih, je uporaba metod GP izredno učinkovita pri reševanju širokega spektra nelinearnih problemov, tudi tistih zahtevnejših.This thesis addresses an overview of applicability of Geometric programming (GP) methods for solving special class of nonlinear logistic problems. Latter can often appear in practice. If they contain posynomial nonlinear criterion function, the GP methods are often most convenient for determination of optimal solutions. First part treats the description of GP methods for unconstrained and constrained problems. The main stress is on the treatment of differential calculus approach, where the corresponding posynomial criterion function must be determined, eventual constraints identified and the degree of difficulty of problem solving must be found. In simpler cases, problems can be solved only by means of analytical calculations. In harder cases, the combined approach of solving must be applied, where numerical methods must be also used besides analytical calculations. In second part, procedures of solving of hypothetical and real problems by means of GP methods are shown. The usage of GP methods is very efficient for solving of broader spectrum of nonlinear problems, even those more difficult