I am never going to make my living by making paper boxes.
Just so you know.
The only class I had today was Modeling and Simulation of the Physical World, or ModSim. Today we met in our studio sections, and once there, we split up into groups of four people. I'm in a group with my roommate (I'm going to call her Carine from this point forward), a boy who was in my Design Nature group yesterday, and another girl with the same name as my roommate.
On the table was a large piece of graph paper (really large -- about 30 inches by 27 inches) and an envelope. The instructions on the front of the envelope told us to choose a team name (we became Carine squared) then set a timer for 35 minutes. We then opened the envelope.
We were given tape, a ruler, scissors, and a task: make paper boxes.
Okay, okay, so there's a little more to it than that. Each box we made would sell for $500 plus one dollar per cubic centimeter in the box. Boxes had to have five sides and be roughly cubical (but it's paper and tape, so roughly is important, there). The first design didn't cost us anything, but if we had multiple designs, each additional one we produced would cost $10,000. Any paper left over at the end would cost us $10 a square centimeter.
So. Boxes.
Our first thought -- the typical first thought, actually -- was "make lots of boxes." If we can make lots and lots and lots of boxes, that's good for profit. We quickly established that our design needed to tessellate so as to minimize the waste, so we ended up with our box nets being L shaped. We split up the labor in a way that we thought was efficient. Carine cut the paper into five inch tall strips, and then I cute those strips into five by two rectangles, which I then cut into Ls. The boy folded the nets, and Other Carine taped the boxes together.
Once Carine finished cutting the strips, she joined me in cutting the rectangles and Ls, and we discovered it was more efficient to cut all the rectangles, then stack them and cut the Ls all at once, since the L is actually the time consuming part.
We had several mistakes. First, we didn't take into account the time it takes to make a box. Smaller boxes means more boxes from the paper, which could mean more profit, but it was probable that we didn't really have time to make that many boxes. Second, maybe cutting all the strips to begin with wasn't a good idea. We really limited our options later. Other teams found that it was worth the cost to change to another design part way through the allotted time. Third, before Carine joined me, I hadn't been cutting in the most efficient way. Fourth, the folding step wasn't really necessary, and it would have been better to just have two people on tape from the very beginning.
As time ran down, eventually we all moved to folding or taping (and also tape distribution along the edge of the table). We made 80 cubic inch boxes, but unfortunately there were lots of L-shaped nets that we cut but didn't have time to make into boxes. This led to a lot of waste, and the result was a very negative profit. In 35 minutes, our box making business lost more than $80,000.
Other teams had more success. The two most successful teams had simply been more efficient at folding. The most successful team had the same kind of boxes we had, but they managed to make 161 of them, more than double our number. The second most successful team made 94 boxes our size and then some that were eight times as large in volume. Several of the other teams weren't as good at making boxes as we were, but they had decided at the end that making one big box with what they had left was a good plan. We hadn't given ourselves that option.
All of this led into our first modeling exercise. For the model, we ignored the issue of waste by assuming that we used all the paper available, assumed that a box of any size takes about the same time to build, and assumed we were making cubic boxes. (Which, by the way, all the teams did.) We were able to express profit solely in terms of the area of paper we were given and the number of boxes, which meant we could graph profit against the number of boxes. It turns out that unless you can make about 60 boxes, you're better off just making 1 big box.
But we made 80, right? So what went wrong? Well, real life didn't follow all those assumptions. We didn't make 80 boxes out of all the material given, and the material that we didn't use counted against us. A more accurate model would include waste, and waste is what hurt us most. But with modeling, you have to start somewhere.
Welcome to ModSim.
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