What we do is charge by day and in some cases lump-sum.
If I understand correctly you have 10,000 parts masked against transparent or white. Depending on size and complexity of objects to be shot, and client budget and end-use needs...
If the parts are small, tabletop size, and simple metal and If I only dedicated two shoot stations, + 2 operators I would estimate about 25-40 work days.
Then there is the matter of clip paths (China), or Masking can be done at time of shoot using reticular screen backgrounds and a simple ring flash. retouch post and organization which would take an additional 10-15 days
I would probably dedicate more resources than that to such a job to get it through the studio faster and save client money.
I would arrange for delivery via secure ftp and establish a standardized naming convention for each item (***This is critical! probably a combination of SKU# + 1st five letters of common name/description + some in-house designate. The rest in metadata field for SEO)
There are many more variables to consider but thats probably a good approximation.
We shoot jobs of that size of grocery store packaging, medical instruments parts, footwear, jewelry, and accessories every year. Its our bread and butter. (We actually shoot bread and butter too! You wouldn't believe how many variations there are!
Price per part, in the end, probably around $25-$70 USD/part shot. But it could be cheaper or more expensive depending on size, location shooting expenses, complexity, post One of my favorite quotes: "Price, Quality, Speed...pick two of those"