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September 20th, 2007, 05:53 AM  #1 
Newbie Joined: Sep 2007 Posts: 1 Thanks: 0  Creating Optimizer  What's the correct Math Model to use?
Hi, I am an application developer and need to create a computer application which output should be the best possible combination of orders that would fit in a a metal stick. I have tried by sorting the order qty in descending order, but found that this approach was very simplistic. I need to know if there is any Math model or formula to make this calculation. Example of what I need to accomplish: I have a metal sticks of 2100 MM (Stick are always the same length) The orders could be of different lengths: 1210 MM 860 " 320 " 650 " 540 " The goal is to cut the orders using the 2100 MM stick by scrapping the list qty of material. In this case the ideal recomendation would be: STICK LENGTH: 2,100 MM =========================================== To cut the stick like this: One order: 1,210 MM & One order: 860 MM Total qty used: 2,070 MM Scrap Qty: 30 MM Someone recomended me to use the Monte Carlo simulation, but I found that this will not work for this scenario. Someone else told me this would be a combinatory analysis, but I am not sure either of this one. I hope you can point me to the right direction. Thanks, Roddy. 
September 20th, 2007, 09:47 AM  #2 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms 
Your problem seems similar to benathan's. This is a binpacking problem, which is NPhard. There are many algorithms that can solve it. In particular, there are PTAS for this problem, so although you can't guarantee that your solution is optimal in 'reasonable' time you can get as close to optimal as desired without spending too long. How many lengths do you have to fit at a time? How many different lengths? 

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