Roll cutting in the curtain industry

Authors:
Arianna Alfieri;Steef L. van de Velde;Gerhard J. Woeginger
Affiliations:
Dipartimento dei Sistemi di Produzione ed Economia dell’Azienda, Polytechnic University of Torino, Torino, Italy;Rotterdam School of Management, Erasmus University, Rotterdam, The Netherlands;Department of Mathematics and Computer Science, Eindhoven University of Technology, Eindhoven, The Netherlands
Venue:
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Year:
2005

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Abstract

We study the problem of cutting a number of pieces of the same length from n rolls of different lengths so that the remaining part of each utilized roll is either sufficiently short or sufficiently long. A piece is sufficiently short, if it is shorter than a pre-specified threshold value δmin, so that it can be thrown away as it cannot be used again for cutting future orders. And a piece is sufficiently long, if it is longer than a pre-specified threshold value δmax (with δmaxδmin), so that it can reasonably be expected to be usable for cutting future orders of almost any length. We show that this problem, faced by a curtaining wholesaler, is solvable in O(n log n) time by analyzing a non-trivial class of allocation problems.