Assortment and Cut of Defective Stocks by Bilevel Programming

In this paper we deal with the problem of deciding the best assortment and cut of defective bidimensional stocks. The problem, originating in a glass manufacturing process, can arise in various industrial contexts. We propose a novel bilevel programming approach describing a competition between two decision makers with contrasting objectives: one aims at fulfilling production requirements, the other at generating defects that, damaging the products, reduce yield as much as possible. By exploiting nice properties of adversarial optimal solutions, the bilevel program is rewritten as a one-level 0-1 linear program. Computational results achieved on random instances with realistic features are discussed, showing the quality and the benefits of the proposed approach in reducing the yield loss from defective material in a worst-case perspective.