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What Is the Cutting Stock Problem?

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  • Written By: Mary McMahon
  • Edited By: A. Joseph
  • Last Modified Date: 16 November 2016
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    Conjecture Corporation
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The cutting stock problem is an optimization puzzle that has important industry applications as well as being of interest to computer programmers and logisticians. In this problem, there are a hypothetical number of rolls of paper of varying widths that must be cut in the most efficient way possible into saleable sheets. Failure to cut the paper efficiently can result in significant wastage, which can translate into very high costs in the real world of industry, where even small margins of error can be substantial.

People have been trying to find the most effective way to cut down bulk stock for centuries, but early exploration of the cutting stock problem and potential formulas to solve it began in earnest during the 1930s. Work on this topic advanced significantly with the rise of computers, allowing for the use of much more complex formulas and other problem-solving tools. Researchers involved with the cutting stock problem also develop products for industry, to put their research to work in a real-world environment.

This problem does not just apply to paper. Many products are manufactured in very large bulk sheets because such production is less costly, but they are not sold in that size to wholesalers, retailers and members of the general public. Some examples include fabric and glass. In addition to being important for industry, the cutting stock problem also can be of concern to individuals. Quilters, for instance, need to think carefully before they cut fabric, to minimize their waste.

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One way to approach a cutting stock problem is through mathematical formulas. This can be a complex challenge, because the elements of the problem might be of varying shapes and sizes. The problem might be set up with multiple rolls of paper at different widths and lengths, for instance. It might also be possible to cut the sheets into different sizes, all of which would be usable for sale; consumers use paper products in a variety of widths, and thus, it wouldn't be necessary to cut everything to one paper size.

Research on the cutting stock problem provides useful material for industry, and industry approaches to the issue can be informative for researchers. With some types of stock, for instance, a small amount of wastage needs to be built in with each cut because the cut edges might not be clean, or some product could be lost during cutting. Brittle, friable materials such as brick do not always cut neatly and might crumble, losing some of their volume and making the cutting stock problem more complicated.

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