The problem is actually somewhat more complex; I didn't want to get into all the gory detail. Before cutting, the cloth is folded in two, so that you cut the left & right sleeves simultaneously; the pattern for the collar is cut in half and put against the fold, so that the (one-piece) collar is cut without a seam. "One-way" stripes and asymmetrical plaids don't work this way when folded, and often have to be cut unfolded. The reason you don't cut an unlimited number of suits at the same time, is that the material is also stacked up in multiple plies -- sometimes 100 plies or more. Large electrically powered vertical knives that look like big jigsaws are used to cut these multiple plies, so that you can cut upwards of 50 suits with the same cut. You now have a classic optimization problem: you have a number of suits to cut, the number of each size of suit follows a "normal" distribution, with the largest number being (American) sizes 40 and 42, and smaller numbers of 36 and 48 sizes, etc. If you try to include too many different sizes into the same group, the efficiency of cloth utilization goes up, but the number of plies is reduced, and hence the efficiency of cutting labor goes down. So there is a material $ vs. labor $ tradeoff. At 10:23 AM 11/1/03 -0500, Bernie Cosell wrote:
On 1 Nov 2003 at 7:05, Henry Baker wrote:
I worked on a computer program to virtually "lay out" ("marking") the pattern pieces on the wool to figure out how much cloth a suit would require. Laying out multiple suits at the same time is typically more efficient in terms of fitting the parts together better, but it is more complex to find all the parts after the cutting process and put them together.
This process is a 2-D knapsack problem, and is obviously very difficult.
Isn't it more complicated than just a 2-D knapsack problem?
Assuming the metric is "yards per suit", it is hard enough figuring out the optimal answer for, say, "three suits at a time", but if you're trying to actually optimize the assembly-line you have to consider that "four suits at a time" or "five..." or "six..." or "forty..." might result in an overall lower average yards-per-suit, so I'd think that that'd make it harder than just a 2-D knapsack [e.g., to determine that doing 87 suits at a time gives you the *optimal* yards-per-suit]
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