Keyword: «runway zone»

The problem of determining the optimal sizes of timber and boards during cutting of saw logs with a brus method is considered, taking into account the Pythagoric and the runaway (parabolic) zones.As a criterion of optimality, the volume of lumber obtained is chosen. The mathematical model is compiled by the classical method and consists of the objective function and the coupling equations. To solve the mathematical model, the method of Lagrange multipliers is used. The numerical method is used to determine the optimal dimensions of the timber and boards. It turned out that with increasing log length, the relative sizes (thickness and width) of boards obtained from the run-off zone increase, and their relative length decreases. When the log length is increased, the relative thickness of the log decreases insignificantly within 0.604 ... 0.584. The total volume of sawn timber obtained from the Pythagoric and the runaway zones decreases with increasing log length.It is more profitable to cut sawlogs according to such a sawing scheme with a shorter log length.