An ACO Algorithm to Solve an Extended Cutting Stock Problem for Scrap Minimization in a Bar Mill.

We introduce the problem of scrap minimization in a bar mill with the capability of cutting several bars at once. We show this problem to be an instance of the cutting stock problem with additional constraints due to the ordering of the layers and relationships between orders spanning more than one layer. We develop an ACO algorithm with a heuristic based on efficient patterns for search space reduction and for tackling the difficulty of building feasible solutions when the number of blocks is limited. We evaluate the performance on actual mill programs of different characteristics to show the usefulness of the algorithm.