## Optimizing Lumber Purchases with Integer Linear Programming

Last weekend, I decided to build a bed. I looked up some plans online, made some modifications, drew up a list of the lengths and sizes of lumber I needed, and went to the store to buy lumber. That’s when the trouble started. The Lowe’s near me sells most of the wood I needed in 6ft, 8ft, 10ft, and 12ft lengths, with different prices. And I needed a weird mix of cuts – ranging from only 10 or 11 inches up to 5 feet. How was I supposed to know which lengths to buy, or how many boards I needed?

Of course, I could have just planned out my cuts on a sheet of paper, gotten close to something that looked reasonable, and called it a day. But I figured there had to be a better way. Turns out, there is, and there’s a huge body of academic literature on the subject. The problem I was facing was simply an expanded version of the classic “cutting stock problem.” It’s a basic integer linear programming problem that can be solved pretty easily by commercial optimization software. So, I decided to try out some optimizations!