Applying parallelogrammic strips for cutting circles from stainless steel rolls

Stainless steel rolls are often cut into circular items to make such common commodities as water jugs, buckets, pails, pots, cups and basins. The items are often cut with the shearing and punching process that consists of three stages. A guillotine shear cuts the roll into sheets at the first stage, and cuts the sheets into strips at the second stage. A stamping press punches out the items from the strips at the third stage. The sheets and the strips may be either rectangles or parallelograms. The height of the sheets is the same as the roll width. A strip contains one or more rows of items, and is parallel to a side of the sheet. This paper presents an algorithm to generate optimal cutting patterns for the three-stage cutting process mentioned above. The algorithm uses a knapsack procedure to generate optimal cutting patterns on the sheets, and uses a linear programming approach to determine the number of sheets cut according to each pattern. The computational results indicate that the algorithm is efficient in both computation time and material utilization.