This is a very tricky area for advanced learners and it is very difficult to formulate advanced rules that account for all instances of use. In this case, 'production', we have a noun used in an uncountable way, so the article would be used to specify some production, and note here that I could have said 'a particular production', which shows that an indefinite article is possible too in some cases.
However, 'production' is a word that carries the notion that the article might specify in its meaning; if I say
production of salt in a particular factory, you automatically know which production, so adding a definite article is possible, but unnecessary. Your reader or listener will automatically assume that you are referring to all that the factory produces. If you said 'part of the production', then, to me, the article becomes necessary because you are breaking the whole up and need to be specific. I am afraid that choices can be made at this level with the articles and it's often on a case-by-case basis. You may well find other people that would use the article and do things slightly differently.
At an elementary level, it's easy to say that if you use the article you should be able to point to which or what you are referring to, but here we have a case where you can point without the article, making it unnecessary.
If there were a straightforward answer and I could cofidy it, I would make a fortune. Sadly, there isn't.
