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2014 Mathematical Modeling and Optimal Blank Generation in Glass Manufacturing
Raymond Phillips, Matthew Woolway, Dario Fanucchi, M. Montaz Ali
J. Appl. Math. 2014: 1-12 (2014). DOI: 10.1155/2014/959453

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 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.

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Raymond Phillips. Matthew Woolway. Dario Fanucchi. M. Montaz Ali. "Mathematical Modeling and Optimal Blank Generation in Glass Manufacturing." J. Appl. Math. 2014 1 - 12, 2014. https://doi.org/10.1155/2014/959453

Information

Published: 2014
First available in Project Euclid: 2 March 2015

zbMATH: 07132018
Digital Object Identifier: 10.1155/2014/959453

Rights: Copyright © 2014 Hindawi

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