The marking for bucking under uncertainty in automatic harvesting of forests

The marking for bucking is the problem of converting a single tree stem into logs in such a way that the total stem value according to a given price list for logs is maximized. Proper marking for bucking is of crucial importance in harvesting of forests. The annual production of saw timber in Scandinavia is tens of millions m 3. Since, furthermore, sawn timber is by far the most valuable forest product in Scandinavia, any improvement in the marking for bucking procedure will yield a large profit. To solve the marking for bucking problem optimally one has to know the whole tree stem. However, it is not economically feasible to run the whole stem through the measuring device before cutting. Therefore, it is a normal situation under computer-based marking for bucking that the first cutting decisions are made before the whole stem is known. In this paper the forest harvesting process will be considered under a general growth curve model useful especially for repeated-measures data. The main objective is to predict the unknown portion y n(2) of the current stem, which will be estimated from the stem data y 1, y 2,…, y n − 1 on the previously processed n − 1 stems and from the known diameter values y n(1) on the current stem. Then a predictor of y n(2) , say y ̂ n(2) , jointly with the known part y n(1) is used in marking for bucking. It turns out that this technique can improve radically the efficiency of harvesting, so that our results provide important knowledge for developing automatic bucking systems of modern harvesters.