An improved bilevel programming approach for assortment and cut of defective stocks

We consider the problem of simultaneously (a) finding a limited assortment of stock items and (b) cutting them with minimum trim loss to fulfill a known demand of different parts. We develop a framework to address the problem when stock sheets can be affected by faults, providing and testing a new bilevel model for both defect occurrence and robust optimization of the production process. The model generalizes an existing bilevel approach and overcomes some of its drawbacks, returning more credible scenarios in terms of defect distributions.