John:

Your promblem is more complicated than stated because you will create an inventory of shorter pieces after the initial cut. The length of these leftover pieces may affect how valuable they are (this is called a utility function).

You will eventually reduce the problem to a maximize a utility function with contraints. If your utility function and your constraint functions are all linear, it should be a straight application of the simplex problem. Otherwise, it is very likely that your problem is NP-complete and thus you will havee an heuristics to solve it. You can probably find heuristics to solve similar problems in Heuristics or Operational Research books. Depending om your Maths background, you may even be able to determine the best/worst/normal case scenarios!

If you provide your utility and constraint functions, I may be able to direct to a specific book.


Daniel