General statement of the optimization problem of flexible delivery

This work opens a series of articles by the authors on optimizing the number of sections of lumber in a set in order to maximize the economic efficiency of their production. The subject of research is dictated by the fact that at present, in large-scale mass sawmilling, almost everywhere there is a displacement of head log sawing equipment with rigid unregulated stands. It is being replaced by equipment with flexible stands, when for each log the optimal setting is automatically set for each log in accordance with its shape and size. To assess the continuity in optimization issues, we turned to the evolution of posts, starting from the theory of maximum posts and ending with modern methods of generating posts, taking into account random sizes and shapes of sawlogs. For this, algorithms and programs developed by the authors for automated design of optimal set-ups and simulation modeling of the processes of sawing logs into lumber were used. As a result, a comparative tentative assessment of the technical and economic indicators of piece-by-piece optimization of flexible sets and group optimization of sets for sawing batches was carried out. It has been established that the flexible set generated for a particular log after measuring its geometric parameters coincided with the optimal set generated for a batch of logs with the corresponding nominal characteristics. However, due to the peculiarities of the size and shape of the log, the volumetric yield decreased by 3.82 %. This reduction does not indicate that the flexible set is less efficient than the optimal set for a batch of logs, since the structures of these sets are absolutely identical. This indicates that the calculated value of the volume output for a batch of logs is 3.82 % higher than the actual one. That is, there is not a decrease in the volume of lumber received, but an error in its forecasting is revealed. Flexible fittings theoretically have no advantages in terms of volume output over rigid fittings. Their effectiveness lies in the simplification of the process of preparing raw materials for cutting due to a decrease in the fractionality of its sorting by diameters or with a complete rejection of it under certain conditions. These conclusions are staged (hypothetical) in nature. In order to confirm and clarify them, the authors develop special simulation models for conducting deeper and more comprehensive studies of the lumber production process using flexible sets. 

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