The use of articles in phrases (upon/by/at request)

[helga23]

Hello!
I've come across examples, in which the use of articles has made me confused. I know, that we have to use a/the before countable possessive nouns (a/the girl's cat, a/the child's toy) and use a/the before countable nouns (a/the request, an/the opportunity etc).Of course, there can be exceptions regarding possessive nouns(a/the children's song, a/the children's playground, a/the women's magazine: compound nouns). And I know perfectly that some nouns can be countable and uncountable at the same time.
But these cases, which I found on the Internet, really confuse:

• Upon customer's request, we offer the most adequte transportation option, in our judgement, taking into consideration relation of transport nad the amount of purchased goods.(the source is context reverso). I can't understand why we a/the isn't used there. As I know, 'customer is a countable noun.
• Sea urchin roe is considered a delicacy and it is used (at customer request) to add strength to ceviche.Wikipedia). I know that 'customer' in this case is an adjective. But why 'a customer request' isn't used there? Request is a countable noun, isn't it? I know that there are such phrases as :at/upon/by request, which are used without a/the, but they have an idiomatic sense. But in this case, I think at customer request means a/the request of a/the customer, isn't it?
• Eviction of temporary residents at request of tenant and members of tenant's family. Why at the request isn't used?
• This mod was developed by request of Marcel Dawson in Qustions & Answers section of LinkedIn. Why not 'the' request?
• The separator can be built on customer request with carbon steel, stainless steel AISI 304, stainless steel AISI 316. Why not on a/the customer request?

I'll be very grateful, If you answer for all my questions. Thank you in advance!

 

[cereal_chick]

First, some comments on your written English (which is very good!):

I've come across examples, in which the use of articles has made me confused.

Usually, I refrain from commenting on people's use of commas, because I only have an intuitive understanding of them myself. However, I would strongly advise against putting a comma there. It's unnatural; jarring, even.

I know, that we have to...

You definitely can't put a comma there.

I know perfectly that

To say you know something "perfectly" is a very odd thing to say; it's also a very boastful thing to say, regardless of how simple the thing you claim to know is. Perhaps you meant to say "perfectly well"? It's much more idiomatic and much less arrogant.

But these cases [...] really confuse

You can say "confuse" without adding a complement, I suppose, but it's very unnatural, and to be frank it's more than a bit pretentious. You'd be better off saying "confuses me".

I can't understand why we a/the isn't used there.

"Why we a/the isn't used there" makes no sense. You could "why we don't use a/the there" or "why a/the isn't used there" instead.

As I know, 'customer is a countable noun.

"As I know" is not a proper way to begin a sentence. Perhaps you mean "as far as I know", which I think gets across what you were trying to say.

I'll be very grateful, If you answer for all my questions.

I wouldn't put a comma there; you can't put "for" there; "if" shouldn't be capitalised as it's not beginning a sentence; and it's a little presumptuous to say you will be grateful if we do answer your questions. It would be better to say "I would be very grateful if you answered all my questions".

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As for your questions:

1. "Upon customer's request" is not correct; you could say "upon the customer's request" or "upon customer request" (without the possessive) to speak generically about what happens when customers request things. "Upon a customer's request" doesn't sound natural when you're speaking generically; it sounds like the lead in to talking about what happened once in the past when a specific customer requested something.
2. "At customer request" is correct. You could add a definite article and a possessive like above to get "at the customer's request" and achieve the same thing less concisely.
3. "At request of" is not correct: it has to be "at the request of".
4. "By request of" is correct.
5. "On customer request" is correct. You could say "on the customer's request".

I think they're just set phrases, the ones that don't make sense to you. I think they just have to be learnt.

[Not a teacher]

EDIT: I note that someone's left a downvote on this comment. Was it a teacher? Was I incorrect or unhelpful in some way? Please do tell me if so; I shouldn't like to not be contributing positively here.