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I'm doing some administration work for an aviation transport company. They build aircraft containers and such here. One of the things they want me to code is a order optimization script that the guys on the floor can use to get the most out of the given material. To give a simple overview: say we order a certain amount beams that are 10 meters per unit. We need beam chunks of 5x 6m, 10x 3.5m, 4x 3m, which are acquired by cutting the 10m in smaller parts. What would be the minimum amount of 10m beams we need to order?

There are some parallels with the multiprocessor job scheduling problem (one beam is a processor, each chunk a job), although that focusses on minimizing the time required to perform all jobs instead of minimizing the amount of processors needed to perform all jobs within a pre-set time. The multiprocessor job scheduling problem is in NP-complete, but I wonder if my variation of the problem is too. Does anybody know similar problems and methods for solving them?

Clavus
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    Someone already solved a similar pipeline cutting problem with [Drools Planner](http://www.jboss.org/drools/drools-planner)(open source, Java). IIRC, he used the traditional approach: First Fit Decreasing with Tabu Search as described in [this quick start](http://docs.jboss.org/drools/release/5.4.0.Final/drools-planner-docs/html_single/index.html#cloudBalancingTutorial). – Geoffrey De Smet Aug 08 '12 at 11:55

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This problem is exactly: http://en.wikipedia.org/wiki/Cutting_stock_problem (more generally http://en.wikipedia.org/wiki/Bin_packing_problem). You can use any old ILP solver. I like http://lpsolve.sourceforge.net/5.5/, its quite friendly to use.

Anil Vaitla
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