Not even the factory that produces, for example, plastic parts for the cars?
Factories have parallel production lines for every part separate? How is that possible?
Well, at the volumes a car is produced at, for plastic parts it's very likely that a factory would be dedicated to making parts only for one vehicle line or manufacturer. Each part needs a dedicated mould and some of these moulds are extremely expensive (dust-bin sized mould, but with fine details) so there may only be a few made.
For instance, most of the plastic parts in my Golf have a 'SPAIN' manufacturing location so I guess either a VW owned factory or subcontractor. VW sold about 500k per year of the Mk7 Golf, so if each car needs 50 x injection moulded parts (whole dashboard is injection moulded now on modern car) then it's easy to see how such a production line would be kept busy pretty much continuously.
And as long as the flow rate is there, JIT works 'fine'. Warehousing even a day's production, especially considering the size of a dashboard or centre console part, would be quite expensive.
An aside: One thing to note is how expensive the finishes applied to dashboard parts are, for instance, which is one reason that it's quite common to find hard, unpleasant plastics in cheaper cars. A lot of effort is expended in finding ways to polymerise the outer skin of the part to give it a pleasant feeling, but some of these finishes have to be hand applied. The so-called "elephants skin" effect on the cheaper models is used to hide moulding defects and thermal sink in such large parts. The quality of plastics in cars has really come along in the last 20 years!