Mathematical Modeling and Optimal Blank Generation in Glass ManufacturingReport as inadecuate




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Journal of Applied Mathematics - Volume 2014 2014, Article ID 959453, 12 pages -

Research Article

School of Computational and Applied Mathematics, University of the Witwatersrand, 1 Jan Smuts Avenue, Private Bag 03, WITS 2050, Johannesburg, South Africa

TCSE, Faculty of Engineering and the Build Environment, University of the Witwatersrand, 1 Jan Smuts Avenue, Private Bag 03, WITS 2050, Johannesburg, South Africa

Received 6 January 2014; Accepted 20 January 2014; Published 27 April 2014

Academic Editor: Aderemi Oluyinka Adewumi

Copyright © 2014 Raymond Phillips et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.





Author: Raymond Phillips, Matthew Woolway, Dario Fanucchi, and M. Montaz Ali

Source: https://www.hindawi.com/



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