Which one is grammatically better?
The material should be issued in parts as small as possible,
The material should be issued in small parts as possible.
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The first sentence
The material should be issued in parts as small as possible
The material should be issued in as small parts as possible
which is a variant of your second attempt would also be fine although it sounds a bit awkward to my ears. I am assuming you left out the first as which I inserted for you.