Guest Post: The Cutting Stock Problem

Prof. Howard Weiss suggests an interesting problem. It is called the “cutting stock problem,” which is often solved using linear programming, the topic of Module B.

What is the major thing that your television, tablet and phone all have in common? They all have a glass display screen. These display screens are all cut from a larger piece of glass known as the Mother Glass.

Mother glass is the largest possible size of glass that can be fabricated that will not break under its own weight. In 1987, the first mother glass, termed Generation 1, was roughly 12 inches by 16 inches accommodating nearly 200 square inches of screen. The latest mother glass, Generation 10, accommodates more than 70 times that amount of screen.

Consider mother glass that is 87 inches by 98 inches for a total of roughly 8,500 square inches. A 65-inch television has a width of 52 inches and a height of 39 inches for a surface area of 2027 inches. If surface area was all that mattered than this mother glass could be used for 8500/2027 = 4 (you have to round down), 65-inch televisions. However, the longer side of a 65-inch television is 52 inches and you cannot fit two of them on top of each other because the mother glass only has 98 inches for its longer dimension. If you make three, 65-inch televisions then you are utilizing 3*2027 inches of the mother glass or only 71% of the mother glass.

The layout chapter (Ch. 9) in your Heizer/Render/Munson textbook describes Assembly Line Balancing. The concepts of rounding down, making 4 televisions in theory, but only being able to make 3 televisions in practice, and utilization are identical to Assembly Line Balancing concepts of rounding down, not always being able to achieve the minimum number of stations and utilization of time, rather than area (square inches).

Fortunately, there are other options that better utilize the mother glass. If you only want to make one size of television, you could make six 55-inch televisions, eight 48-inch televisions or eighteen 32-inch televisions, each of which utilizes over 90% of the mother glass. In addition, you do not have to make only one size of screen on the mother glass. For example, glass could be cut as shown in the diagram above that includes both 55-inch televisions and 65-inch TVs.

Classroom discussion questions:
1. What is the largest single panel LCD that is currently manufactured? (Check it out on-line)
2. Using graph paper determine how many 83-inch and 32-inch televisions could be cut using the Mother Glass dimensions above.