Influence of production costs on cutting optimization in window frame production—A graph-theoretical model

Window lamellae are the raw materials used for building wooden window frames. The frames are produced using two types of cut lamellae: one type is cut to pre-specified lengths, the other type is cut to variable lengths and then finger-jointed. The lengths of cut lamellae are in turn produced from raw lamellae which are optically scanned for defects prior to cutting.Cutting plans are generally optimized using the scanned information, to maximize total lamella value. We test an alternative approach that deducts cutting, finger-jointing and gluing costs from cut lamellae value, and optimizes net production value.Both optimization approaches are modeled using networks with vertices representing potential cutting positions and arcs representing potential cut lamellae. The value of each arc is determined by the length, type and quality class of the potential lamella and, in the case of the net product value optimization, is reduced by the production costs. The optimal solution, computed using dynamic programming, corresponds to the longest path in these acyclic digraph networks.The two optimization approaches were compared using 148 raw lamellae. The optimization of total lamellae value resulted in an overall lamellae value of 275,988 and a corresponding net production value of 275,930, whereas the optimization of net production value results in an overall lamellae value of 269,242 and a net production value of 269,415. The results were significantly different using a paired t-test and represented an improvement in production value of 0.06%. As expectations of the company involved were much higher than achieved by this study, it is demonstrated that the inclusion of production costs in optical scan and cutting systems in window frame production only has the potential to increase production value on a small scale.