Application of the linear programming to optimizing wood extraction in thinnings

Improvement cuttings conducted simultaneously on a few closely located areas, often face problems about how to prepare places that would serve as temporary landings for the harvested wood. This results from insufficient wood storing space in the forest and limited accessibility of the road network to wood hauling trucks, and leads to solutions, suggesting where small landings at tree-stand edge must be established, often in places rather distant form the thinning plots. When the wood is harvested on several thinning plots and should be transported to several small landings, a problem appears, where (i.e. to which landing) should the wood from a particular thinning plot be sent. The paper presents a model to solve this problem using the simplex algorithm, which is used in linear programming, a method applied in operations research. The wood was sourced from 15 thinning plots and 11 wood landings were located. In the model, the objective function presented total transportation work, to be spent on the wood extraction. The objective function was minimized. The problem was set up on the Excel spreadsheet and then resolved with the solver application. The model enabled to direct the harvested wood from different thinning plots to different landings in an optimal way. The results enabled to design the optimal wood extraction routes and to determine the allowable changes in the amounts of wood harvested from each thinning plot, which would not change the optimal solution. The model enabled also to calculate the minimum amount of transportation work, which would be spent during the optimized transportation of wood form particular thinning plots to particular wood landings.