A two-criterion mathematical model for optimizing the fractional sorting of logs by thickness

The article is devoted to the problem of sorting logs by thickness when forming sawing batches with optimal selection of sawlogs by diameter groups. Based on maximizing the volume output, science focuses production on high fractional sorting of logs by thickness through one even diameter. Manufacturers give a clear preference to coarser log sorting through two to three even diameters, seeing the cumbersome and costly sorting with high fragmentation and not finding the promised increase in the volumetric yield of lumber. Almost all sawmill scientists paid attention to the issues of fractional sorting of logs by thickness. Despite the differences in approaches and proposals, what they have in common is that the volumetric yield of lumber is traditionally considered to be the optimality criterion. The purpose of these studies is to prove the feasibility of using the profitability of lumber production as a criterion for the optimal structure and parameters of a large-scale sawmill enterprise, since it takes into account not only the volumetric yield of lumber, but also the cost at which it is achieved. To achieve the goal and solve the problems arising from it, questions arise that are not answered by the general theory of sawmilling, since in it the log is represented as a paraboloid of revolution with nominal dimensions. Therefore, the authors proposed a variant of the development of the theory of cutting logs, taking into account the random variability of curvature, ellipticity and accuracy of the location of logs.

Mathematical models that connect the probabilistic characteristics of logs and their cutting processes with the volumetric yield of lumber and the profitability of the sawmill were obtained.

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