The Task of Lumber Dressing Plan Optimization, Its Versions and Applications
Schepalov Sergey, Professor Kuznecov Vladimir Alekseevich (Petrozavodsk State University, Russia)It is a classical task of roundwood length cutting into saw-timber by rectangular cross-section of reference dimension. Problem definition: it is required that some set of equal length, width grouped stems should be longitudinal cut into fixed shape saw-timber. Cutting knifes have some fixed width.
Linear optimization method with scheme of column generation according to maximization criterion of difference between used raw material usefulness function and generated production forms the basis of task decision algorithm. On each iteration of the simplex algorithm the sub-task of flat cutting is solved by searching of optimum estimation of sawing scheme application by two-dimensional dynamic programming method. Linear dependence of variable dual estimation at any step from respect column of first step restriction matrix allows to use given method and to vastly restrict calculation time.
At present, program complex implementing described algorithm of sawing scheme and its application activity estimation is developed in PetrSU.
