PC-Implementation of 1-& 2-dimensional Cutting Stock Heuristics

Abstract

To implement a cutting stock algorithm on a Personal Computer one aim of the development is the reduction of complexity. The amount of data generated by the algorithm and the required computation time have to be compressed. By the random selection of good patterns we reduce complexity in the framework of the Haessler heuristic (1975). In this heuristic the algorithm is governed by serveral measures: the number of required stocks to complete the total order, the percentage of the current demand to be satisfied by a multiple application of one pattern (using level) and the percentage of trim loss. The orders not satisfied so far are sorted by the number of demanded pieces. More generally this sort can be considered as priority rule applied to the open orders. The computational experience of our approach is based on 10000 randomly generated problems with 4 to 8 different orders. The ordered length varied between 9% and 49% of the stock length. This stock length ranged from 100 to 200 length untis. The computational experience exhibites solutions of high quality in the region of 3% trim loss yielding some evidence for the thesis that good patterns are lying densely in the solution space. On the basis of the 1-dimensional case we construct the 2-dimensional heuristic with the approach of Guillotine-cuts. With this approach we get a trim loss in the region of about 20%. This higher trim loss is due to the 2-dimensionality of the problem.