Statistical properties of the apportionment degree and alternative measures in bucking outcome

In the harvesting technique prevailing in Scandinavia, tree stems are converted into smaller logs immediately at harvest. Modern sawmills attempt to operate according to customers' special needs rather than only minimize production costs. Since the annual production of saw timber in Scandinavia is in tens of millions of cubic meters, proper measuring of the goodness of the bucking outcome is of crucial importance, The outcome of the bucking operation can be considered as a multidimensional table of tree species, quality grades, prices and length and diameters classes. The prevailing method to measure the outcome is the so-called apportionment degree, which is calculated from the relative portions of the observed and target tables. However, this measure has severe drawbacks. E.g. it gives the same weight for each log class. Therefore, for example, the effect of the shape of the distributions is completely ignored. In this study we present some basic results of the statistical properties of the apportionment degree and present some alternative means to measure the bucking outcome. Also a simulation study is carried out to illustrate the relative performance of the measures presented.