we will delivery all the compressors at/on site…
I would say “we will deliver [not delivery] all the compressors to the site…”
I would not say “at site.” I would say “on site (or on-site)” or “at the site.” The meanings are essentially the same; there are some subtle differences but I’m at a loss to explain them quickly.
I’ll see you at the museum is a grammatical Standard American English construction. *I’ll see you at museum is not. Contrast I’ll see you at Joe’s, which is grammatical.
Saying that you “will arrange to have the compressors at the site by by January 12, 2012” would be grammatical, but wordier than the proposed text.
If you specify “at site” for delivery of something, you are liable to find it outside the gate when you arrive in the morning. If it says “on site”, the delivery guy will wait for you and put it where you want it. If the delivery is gravel, the difference is substantial. In certain circumstances the terms are not interchangeable or the result of funky grammar, they can mean different locations.
Idiomatic English also drops definite article the for certain locations that are part of one’s routine, so we do say: at school, at work, at church, etc.
IMHO “on site” (often used adjectivally and hyphenated) always, always refers to action taking place on the site of the entity doing the action, as opposed to taking place elsewhere, and is pretty much entirely unrelated to deliveries to that site.
In American usage, I would never* say “will be delivered on site,” or “at site,” but pretty much exclusively use “Will be delivered to the site.”
*Possible exception for a different use of the word “delivered” – I would say “Because there was no time to drive to the hospital, the baby was delivered on-site right here at our company.”
“The parts were delivered to the site so that we could conduct on-site repairs rather than send our computers back to the manufacturer.”
I tend to disagree with your hyphenation here. I would only hyphenate this phrase if I were using it as an attributive adjective: “on-site delivery of the baby”, “on-site training”. Otherwise I would see it as a two-word adverbial phrase: “The training was delivered on site”; “The cement was delivered to site”.
I’ve never heard “on site” used on anything that was not entirely contained in the site. In other words, if something was delivered on site, I would assume it meant someone delivered something from one part of the site to another, without involving someone off site, like a mail carrier.