Harvest volume optimization with linear programming

The paper presents a linear programming method of harvest volume determination including calculations of net present value (NPV) of standing timber. NPV was computed taking into account the costs of harvesting and skidding and a discount rate of 2.5%. Harvest volume was determined for three 10-year management periods according to the following four scenarios: (1) Vol_max - timber volume maximization within constraints concerning harvest area (4 ha), cutting interval (5 year), felling a maximum of two adjacent cutting plots over a 10-year period, combined harvest area per decade (a quarter of the total area of near-mature, mature, and overmature stands), and minimum stand age (starting with near-mature stands); (2) RA - as in the Vol_max scenario plus the harvest area per decade should be smaller than or equal to the regulated area; (3) NPV_max - NPV maximization while respecting all constraints from the Vol_max scenario; and (4) IUL - pursuant to the Instrukcja. [2012]. Calculations included allowable cuts by maturity for mature stands (the last age class) and near-mature and mature stands (two last age classes), as well as the allowable cut for mean age equalization. Subsequently, the optimum allowable cut was determined and particular stands were designated for felling, starting with the oldest ones, and taking into consideration spatial layout. An optimization case study was done for the Seredzice forest unit designated for clearcutting, consisting of pine stands or stands with a predominance of Scots pine growing on coniferous and mixed coniferous habitat types with a total area of 813.20 ha in the Marcule Forest District (C Poland). The total harvest volume determined using linear programming for a 30-year period was 81.17, 74.70, and 80.84 thousand m3 in the Vol_max, RA, and NPV_max scenarios, respectively, which was greater by 29%, 19%, and 28% than in the IUL scenario (62.95 thousand m3). The total NPV of stands designated for harvesting in the 30-year period was 9423, 8824, and 9483 thousand PLN for the Vol_max, RA, and NPV_max scenarios, respectively, as compared to 7492 thousand PLN in the IUL scenario. The simultaneous determination of harvest volume for several management periods by analyzing the parameters of individual stands and selecting the optimum harvest period for them makes it possible to better exploit the production potential of the forest and increase both the volume and value of the harvested timber over a long time horizon.