how to do that in order to achieve the littlest waste?
Cutting each rod into one of each (3+4+5) = 12, so there is no actual waste.
I think you meant that you have a certain number of each length that you
need to cut, and you want to use the least amount of rods. Is that correct?
One technique is to use another program to generate the different possible
patterns. I count 7 patterns. For example, pattern #1 would cut two 5m
lengths. Pattern #2 would cut two 3m lengths, and one 4m length.
You than have Solver pick an Integer amount of each pattern. One constraint
is that the total # of 3m cuts >= your requirement, etc...
You "minimize the total # of patterns used. Here are the patterns that were
generated:
{5, 5},
{3, 3, 4},
{3, 3, 5},
{3, 4, 4},
{3, 4, 5},
{4, 4, 4},
{3, 3, 3, 3}}
Here is just one technique. I usually have Solver do this in a loop and
generate a few solutions. Usually for a problem of this type, you will have
multiple solutions. Say for example that the solution is a total of 10
patterns (using 10 rods). You will most likely have two of more solutions
that use 10 patterns/rods.
Suppose one solution left 3m of waste on 1 rod, and another solution left 6m
of waste on another rod. Solution #1 has the "least" amount of "waste."
However, you may want to consider solution #2. Now, suppose later, that one
of your 4m cuts was defective. You need to make another one. With solution
#1, you need to cut from a new rod. However, with solution #2, you can use
the leftover 6m length to cut your 4m length, and no additional rods were
used. Basically, this comes down to an "art" instead of a "science" at this
point. Just something to think about when discussing minimum waste.
HTH
Dana DeLouis
