Width-Packing Heuristic for Grouping in Two-Dimensional Irregular Shapes Cutting Stock Problem

Abstract

This paper investigates cutting stock problem with fixed number of weakly heterogeneous shapes and multiple open-dimension stock sheets having fixed width and variable length with the objective of minimizing the stock sheet wastage. The research is based on the hypothesis that creating groups of shapes and mapping the generated groups on heterogeneous stock sheets leads to improved utilization, compared to using single stock sheet. A width-packing heuristic for shapes grouping has been proposed, which generates feasible groups considering width margin of stock sheet along with length and overlap margin of shapes. The groups are mapped onto stock sheets using column generation method by replicating each shape in the group multiple times such that aggregate length of all shapes in group results in minimum trim loss along the length. Linear programming approach is used to select the minimum number of stock sheet layouts that can fulfill the quantity requirements of shapes. Comparison with the existing commercial system shows that the proposed technique achieves up to 3 % improved utilization for all input samples where rectangular enclosure utilization of shapes is high.