Technical Note—The Silver Anniversary of an Optimization Result in Rolling-Mill Practice

In cutting beams or candy or rulers to a specified length, it is often sensible to make a first rough cut comfortably long and then a second exact cut. This certainly applies to the hot-rolling of steel beams, where the first cut is made as the continuous beam emerges from the rolls and the second made after straightening and cooling. The waste from odd ends is reduced if the first cut is close to the specified length, but this procedure involves the risk of an occasional beam being too short, which is serious if such a short beam is completely wasted. This last assumption is often realistic, for example, where recycling or sale as a remnant is excluded by reason of secrecy, safety, or price. The problem we solve is how to control the rough length so as to minimize the total waste. A graphical solution for a normal distribution of the rough length was published 25 years ago. Here we give an analytic solution for any distribution and a numerical realization, using standard tables, for a normal distribution.