Of your three choices, "plastic producing factory" appears 3 times on Google, "plastic production factory" appears 16 times, and "plastic factory" appears 6,070 times.
"PlasticS factory, however, makes the strongest showing; it appears in 8,560 entries.
As you know, compound noun phrases are often made with one noun acting as an adjective. Since it is an adjective, it is singular. Examples of this kind of structure are "shoe store," "automobile parts," and "student loan."
There are exceptions to this kind of construction, however, in which the "-s" appears on the first noun. Examples of this structure are "antiques show," "parts department" and "communications specialist." One of the reasons for adding an "-s" to the first noun may be to clarify the expression which might otherwise be ambiguous. For example, "an antiques show" clearly shows that the show is made up of antiques, and is not an old, ancient show. "A plastics factory" indicates that the factory makes plastic materials, and is not itself composed of plastic.
The structure of compound noun phrases seems to be in flux.