One-dimensional stock cutting resilient against singular random defects

When industrial components are obtained by cutting bars of raw material (stocks), production volumes and values can be affected by random defects in the stocks. To deal with this inconvenience, we propose to design reconfigurable cutting patterns that can be adjusted so that defects fall, as far as possible, in the residual area that is normally discarded. In this situation, a trade-off arises between the amount of this scrap area and the probability that there exists a reconfiguration with no loss of items. We define mathematical models for the expected economic value produced with a single stock (or with all the stocks cut to obtain the required items). We then introduce the relevant optimization problems, discuss their complexity and devise various solution algorithms, comprising dynamic programming and Integer Linear Programming. The effectiveness of our algorithms is finally illustrated by computational tests on sample problems derived from the literature.