A practical approach for determining rectangular stock sizes

This paper addresses the problem of determining what rectangular sizes should be stocked in order to satisfy a bill of materials composed of smaller rectangles. As is common in many manufacturing operations, the stock material will be cut using two-staged guillotine cutting patterns. The paper first generates a large number of stock sizes ideally suited to the bill of materials. Then it uses a facility location algorithm to consolidate the stock sizes down to an acceptable number. Given the solution of what rectangular sizes to stock, a second program is used to map bills of materials into the stock rectangles. The effectiveness of the approach is demonstrated by generating stock sizes for a real-world bill of materials with 392 distinct order sizes and over 7700 order pieces.