Mogućnosti primene linearnog programiranja u planiranju gazdovanja šumama

Abstract

U situacijama kada je potrebno razmotriti različite opcije prilikom donošenja odluka u šumarstvu (i generalno), pri čemu na izbor utiču teško uporedivi kriterijumi i brojni međusobno suprotstavljeni interesi, mogu se primeniti metode višekriterijumskog odlučivanja. Jedan od metoda koji pripada ovoj oblasti, a primenjuje se i u šumarstvu, jeste matematičko programiranje (posebno linearno programiranje). Linearno programiranje ima dugu tradiciju primene u američkom i evropskom šumarstvu, dok je u šumarstvu Srbije još uvek teorijska, a pogotovo praktična nepoznanica. Stoga je u ovom radu analizirana mogućnost primene metoda linearnog programiranja pri izradi plana seča obnavljanja u zasadima topola GJ 'Topolik' kojom gazduje JP 'Vojvodinašume'. Upotrebom ciljne funkcije (linearnog programiranja) i odgovarajućeg softverskog paketa dobijen je maksimalan prinos koji se može realizovati sečom plantaža topola u uređajnom periodu 2012-2021. god u iznosu od 155.852 m3,, pri čemu je ispunjen unapred postavljen uslov da prinos bude izjednačen po polurazdobljima (I polurazdoblje 77.925 m3, II polurazdoblje 77.927 m3). Maksimalan prinos dobijen po ovoj metodologiji manji je za 4.040 m3 od teorijski mogućeg prinosa koji bi se dobio kada bi svi odseci bili posečeni na kraju drugog polurazdoblja, odnosno veći je za 8.430 m3 od prinosa koji bi se dobio sečom odseka na početku uređajnog perioda. Dobijeni rezultati i strana iskustva u ovoj oblasti nedvosmisleno ukazuju na to da se linearno programiranje može uspešno koristiti i za rešavanje i znatno kompleksnijih problema (u odnosu na prezentovan u ovom radu) u našoj šumarskoj praksi (višedimenzionalno planiranje sa nizom ograničenja).

In situations where it is necessary to consider a variety of options when making decisions in forestry (and in general), with the choice influenced by hardly comparable criteria and a number of conflicting interests, a possible solution is to use multiple criteria methods. One of these methods, which can be applied in forestry, is mathematical programming (in particular, linear programming). Linear programming has a long tradition of being used in the U.S. and European forestry, whereas in the forestry of Serbia it still represents a theoretically and practically unknown tool. Therefore, in this paper we analyze the possibility of applying the methods of linear programming in developing a plan of regeneration cutting in the poplar plantations of FMU 'Topolik' managed by PE 'Vojvodinašume.' Using the aimed function (linear programming) and the corresponding software package the maximum yield that can be achieved by cutting the plantation was obtained. The planned management period was from 2012 to 2021 and its volume was 155 852 m3. The preset condition that the yield in half-periods remains equal was fulfilled (half-period I 77,925 m3, half-period II 77,927 m3). The maximum yield obtained with this methodology was by 4,040 m3 lower than the theoretically possible yield that would be obtained if all stands were cut down at the end of the second half-period, i.e. higher by 8,430 m3 than the yield that would be obtained if cutting of the stands were performed at the start of the management period. The results obtained and foreign experience in this area clearly indicate that linear programming can successfully be used to solve this problem and even more complex problems (than the one presented in this paper) in our local forest practice (multidimensional planning with a series of constraints).