This paper discusses the stock size selection problem (Chambers and Dyson, 1976), which is of relevance in the float glass industry. Given a fixed integer N, generally between 2 and 6 (but potentially larger), we find the N best sizes for intermediate stock from which to cut a roster of orders. An objective function is formulated with the purpose of minimizing wastage, and the problem is phrased as a combinatorial optimization problem involving the selection of columns of a cost matrix. Some bounds and heuristics are developed, and two exact algorithms (depth-first search and branch-and-bound) are applied to the problem, as well as one approximate algorithm (NOMAD). It is found that wastage reduces dramatically as N increases, but this trend becomes less pronounced for larger values of N (beyond 6 or 7). For typical values of N, branch-and-bound is able to find the exact solution within a reasonable amount of time.
"Mathematical Modeling and Optimal Blank Generation in Glass Manufacturing." J. Appl. Math. 2014 1 - 12, 2014. https://doi.org/10.1155/2014/959453