The delay could have caused/resulted in order cancellation by the customer.

however, if you leave the structure as is, then you have it right: "resulted in customer canceling the order"

"resulted in customer's canceling the order" - это вообще на каком языке? турецком??
зачем апостоф?
As the result of the delay the customer was about to cancel the order

http://grammartips.homestead.com/possessivewithgerund.html

Внизу список правильных и неправильных вариантов.

Начнем с того, что cancelling с двумя l пишется. Ваш вариант невероятно коряво звучит, уж праститэ.

Dictionary: can·cel (kăn'səl)
v., -celed also -celled, -cel·ing -cel·ling, -cels -cels.

http://www.answers.com/cancel

2. Я для аскера отметил грамматическую ошибку (переводить я бы так не стал). Но по собственно грамматике у Вас есть какие-нибудь аргументы? Если нет, признайте это.

"Спокойствие, ТОЛЬКО спокойствие!" (с)

Mike you know what 'hater base' is? :)

1. Professor Villa was amazed by her students working as hard as they did.
2. The class working collaboratively was somebody else's idea.
3. It was a case of old age getting the better of them.

Коньтекст, кароче.

А лучше, конечно, предложение сформулировать по-другому.

When the noun preceding the gerund is plural, collective, or abstract, use the common form of that noun, not the possessive.

1. Professor Villa was amazed by her students working as hard as they did.
2. The class working collaboratively was somebody else's idea.
3. It was a case of old age getting the better of them.

Думаю, что примеры коллеги Kid взяты из какого-нибудь электронного учебника/справочника по грамматике не британского происхождения. Может американского ... . Это один из, так называемых, "dubious cases".Т.е. все три примера нельзя считать однозначно "gerundial constructions".
В первом и втором примере working можно рассматривать в качестве причастия-1 в функции определения существительных students и class, а в третьем примере getting причастие в такой же функции определения существительного age.
Но, при этом, оттенок и свойства герундиальности в этих предложениях полностью не пропадает.
Все зависит какой смысловой акцент делает говорящий или любой человек, использующий это предложение (в том числе и не носитель языка или переводчик на другой язык).

http://www.bartleby.com/64/C001/028.html#GERUNDANDPOS

gerund and possessives (fused participle). Some people insist that when a gerund is preceded by a noun or pronoun, the noun or pronoun must be in the possessive case. Accordingly, it is correct to say I can understand his wanting to go, but incorrect to say I can understand him wanting to go. But the construction without the possessive, sometimes called the fused participle, has been used by respected writers for 300 years and is perfectly idiomatic. Moreover, there is often no way to “fix” the construction by inserting the possessive. This is often the case with common nouns. Thus you can say We have had very few instances of luggage being lost, but not … of luggage’s being lost.

i.e. resulted in the customer cancel(l)ing the order

Dear SirReal, you write the following.

правильно: "resulted in customer's canceling the order"

This is grammatically INCORRECT and completely wrong. There is no need for an apostrophe + S ('s) here. The original sentence was not incorrect as you said, but was correct.

I am a NATIVE English speaker, TEACHER of English and TRANSLATOR. Trust me, I am correct, irrespective of any links to grammar websites or quotes from grammar books you may post here.

Adam, can you actually construct an argument or am I supposed to be awed by your using CAPS?

As far as I can tell, you signed up on this forum because someone told you about this particular forum topic and asked you to submit a posting to prove me wrong.

Your using caps doesn't hurt me - it merely highlights your lack of arguing skills.

You have yet to prove anything to me.

This is roughly correct: "resulted in customer cancel(l)ing the order" (needs THE)
This is incorrect: "resulted in customer's canceling the order"
In addition this is correct: "As a result of the delay the customer was about to cancel the order"
This would also be correct: "This resulted in his/her cancel(l)ing the order" (possessive pronoun) - although this is a less common construction

By the looks of it though, it was a mistake posting an answer here in the first place. In future I will not bother to answer.

I construe "Adam, can you actually construct an argument or am I supposed to be awed by your using CAPS?" to be incredibly rude, unnecessary and arrogant. It strikes of someone who has been told that s/he is wrong and does not like it, most likely someone who has a high post count on the forum and does not like a newcomer justifiably challenging his/her responses.

I was not attempting to construct an argument, I was merely highlighting two sentences - one as being correct, one as being incorrect. In addition, I was telling you who I am so that you can have an element of trust in the response that I provided. I do not see that I have done anything wrong.

I do not see that conducting this disagreement here is useful or constructive - neither for the original poster nor those who are reading and looking for answers. I hope that the information that I have provided has been useful to someone here, but I can clearly see that my help and advice is not welcome. Strange, I thought that this was an open forum.

Good evening.

If you wish to continue to dish out incorrect advice then please be my guest, but you will not be doing yourself, nor others, any justice.

You're not even a Russian-English translator. Admit you came here on someone's tip-off and then we'll talk.

I am not attempting to start an argument. I felt that I should post something on this topic as there seemed to be an awful lot of discussion on it. I thought some input would be appropriate and even welcomed - I did not expect to come up against a wall, in yourself, preventing me from bringing across a point of view.

I'm sorry but I have more important things to do than argue on here with someone that I don't know. Indeed I also have more important things to do than act on a 'tip-off' from someone on a Saturday night - I don't know anyone on this forum, as far as I know, and I wouldn't set out merely to tell someone that they are wrong. I don't understand why someone would tell me to come here merely to argue with you - it doesn't sound like my idea of a fun evening.

You are correct in that I am not a Russian-English translator, but then I never said that I was. I am, nevertheless, a translator.

Good evening, again, I shall not darken your door again.

Ido apologize for our colleague´s arguing.
He is a good guy, trust me.

Please stay at our forum. Don't leave!
We really need more teachers of English - especially native speakers - here, on the forum.