Business Applications of Operations Research

CHAPTER 10

Paper Roll Trimming

Steel, paper, and textiles are produced in long rolls of different widths. These rolls need to be sliced to appropriate lengths to satisfy requirements of fabrication of machinery or paper cartons or apparel. For example, an 8 feet width roll could be sliced to obtain rolls of 5 feet and 3 feet width as shown in Figure 10.1. Slicing has to be done in a manner such that the total cost of material used is minimized.¹

Figure 10.1

Let us take the example of three paper rolls: one of 1000 feet length and of 8 feet width, another of 500 feet length and of 5 feet width, and a third of 600 feet length and 3 feet width. We ...