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Arkusz kalkulacyjny Microsoft Excel 5.0 wykorzystano do rozwiązania zadań z programowania liniowego. Sposób wypełniania arkusza oraz definiowania problemu w oknie Solver-Parametry został zaprezentowany na przykładzie optymalizacji transportu słomy w przedsiębiorstwie rolnym. Procedura wypełnienia arkusza jest prosta i nie wymaga wykształcenia informatycznego, a wykorzystanie standardowych funkcji SUMA.ILOCZYNÓW oraz SUMA, zwłaszcza w przypadku programowania z dużą liczbą zmiennych decyzyjnych, powoduje dobrą widoczność wszystkich danych i daje możliwość szybkiej ich modyfikacji bez żmudnych przeszukiwań w długich formułach.
The objective of the study was to optimize wood extraction from a clear−cut area to several upper landings located at roads suited for wood haulage in a situation where the room for storing the wood was limited. The optimization process was to divide the clear−cut area into zones, from which the wood assortments should be transported to the different landings, so that the total transportation labour would be minimized. The research was conducted in Oborniki Forest District (western Poland) on a clear−cut area where the harvest of 2027 m3 of wood in four assortments was planned. The optimization method used presented a linear programming problem, which was formulated and solved with the Solver tool, available with a common spreadsheet. The clear−cut area was divided into a number of elementary plots, for which the quantities of the wood to be extracted and distances to the specified landings were determined. Altogether 189 such plots were defined, mostly square in shape and with 20 m long side. Three upper landings for each wood assortment, located at roads accessible to long−distance vehicles were also determined (fig. 1). The minimization of the transport labour needed for the extraction of different wood assortments was set as the criterion for the objective function. The results of the calculations, after putting them on the forest clear−cut area map (fig. 2), provided information about parts of the clear−cut area to which the wood should be extracted to. As it was expected, in the majority of cases, the model directed the wood to the landings, which were the closest, but in case of one assortment, the wood was directed to the landing located a bit further away than to the closest one. The model enabled to minimize the transportation labour spent on wood extraction from the clear−cut area. The calculations did not require any specific applications, enabling users of commonly available spreadsheets, equipped with a Solver tool to perform such calculations.
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.
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