Mathematical Modeling and Optimal Blank Generation in Glass Manufacturing

Abstract

This paper discusses the stock size selection problem (Chambers and Dyson, 1976), which is of relevance in the float glass industry. Given a fixed integerN, generally between 2 and 6 (but potentially larger), we find theNbest 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 asNincreases, but this trend becomes less pronounced for larger values ofN(beyond 6 or 7). For typical values ofN, branch-and-bound is able to find the exact solution within a reasonable amount of time.