The one dimensional cutting stock problem using two objectives

This paper considers the cutting stock problem with two objectives. The primary objective is to minimize the trim loss in a given piece of metal work requiring metal sections of various lengths. The secondary objective is to organize the cutting so that the maximum quantity of leftovers is accumulated in the last bar(s). This leftover will then be of a length allowing it to be used in the future. An algorithm which provides an optimal solution is presented for this problem. However, it may not be efficient for large problems. Consequently, a heuristic approach is suggested, with the large problem being divided (decomposed) into smaller ones: the remainder of one problem being used in the next. This model was developed for a small metal workshop in a kibbutz.