Mathematical modeling and optimal blank generation in glass manufacturing

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. © 2014 raymond phillips et al.