Should Pilgrims Offer Udhiyah?
Question

Is the udhiyah obligatory for the pilgrim doing Hajj?
Praise be to Allah.Is udhiyah obligatory for non-pilgrims?
The scholars differed concerning the ruling on the udhiyah . The majority of scholars are of the view that udhiyah is Sunnah mu’akkadah (a confirmed Sunnah), and others are of the view that it is obligatory for the one who can afford it. 
This difference of opinion has to do with people other than the one who is performing Hajj. 
Udhiyah for pilgrims
As for the pilgrim, the scholars differed as to the ruling on offering an udhiyah in his case. Some say that it is prescribed – whether they regard it as mustahabb or obligatory, and others said that it is not prescribed. 
 Why udhiyah is not recommended for pilgrims?
Those who say that the udhiyah is not prescribed for the pilgrim differed as to the reason for that, and there are two opinions: 

Because there is no ‘Eid prayer for the pilgrim, and his sacrifice is the hadiy of tamattu’ or Qiran
Because the pilgrim is a traveller, and the udhiyah is prescribed for those who are not travelling. This is the view of Abu Hanifah, according to whom if the pilgrim is one of the people of Makkah, then he is not a traveller, so it is obligatory for him to offer the udhiyah.

Detailed views of the jurists
There follow details of their views and some of their comments. 

The Hanafis. It says in al-Mabsut (6/171): 

“It is obligatory for the one who can afford it and for non-travellers in our opinion.”
In al-Jawharah al-Nayyarah (5/285, 286) it says: 
“It is not obligatory for the pilgrim who is a traveller. As for the people of Makkah, it is obligatory for them even if they do Hajj.”

The Malikis. They said that the pilgrim does not have to offer an udhiyah because he is a pilgrim, not because he is a traveller. 

In al-Mudawwanah (4/101) it says: 
“Malik said to me: The pilgrim does not have to offer an udhiyah even if he is one of the inhabitants of Mina once he is performing Hajj. I said: Do all people have to offer the udhiyah according to Malik’s view except the pilgrim? He said: Yes.”

The Shafi’is said it is mustahabb to offer the udhiyah for the pilgrim and for others. 

Imam al-Shafi’i (may Allah have mercy on him) said: 
“The Makkan pilgrim, the one who is in transit from one country to another, the traveller, the non-traveller, and the male and female who can afford an udhiyah, are all the same and there is no difference between them. If it is obligatory for each one of them then it is obligatory for all of them and if it is waived for one of them then it is waived for all of them. If it is obligatory for some of them and not others, then the pilgrim is the one for whom it is most likely to be obligatory, because it is a sacrifice and he has to offer a sacrifice, whereas others do not have to offer a sacrifice. But it is not permissible to make something obligatory for the people without proof or to differentiate between them without the same.” Al-Umm (2/348) 

Ibn Hazm (may Allah have mercy on him) said: 

“The udhiyah for the pilgrim is mustahabb as it is for non-pilgrims. Some people said: The pilgrim does not offer an udhiyah. The Messenger of Allah (peace and blessings of Allah be upon him) encouraged offering the udhiyah, so it is not permissible to deny the pilgrim the virtue and possibility of drawing closer to Allah without a text to that effect.” Al-Muhalla (5/314, 315) 

According to the Hanbalis, it is permissible for the pilgrim to offer an udhiyah. 

Ibn Qudamah (may Allah have mercy on him) said: 
“If he does not have a hadiy (sacrificial animal) with him, and he has to offer a hadiy because it is obligatory for him, then he should buy it. If it is not obligatory for him, but he wants to offer an udhiyah, then he may buy an animal that may be offered as such.” (Al-Mughni, 7/180) 
In the hadith from ‘Aishah (may Allah be pleased with her) it says that the Prophet (peace and blessings of Allah be upon him) offered an udhiyah on behalf of his wives in Mina during the Farewell Pilgrimage. (Narrated by al-Bukhari (5239) and Muslim (1211) 
Some of the scholars – such as Ibn al-Qayyim – rejected this interpretation of the hadith and said that what was meant by udhiyah here was the hadiy.  (Zad al-Ma’ad, 2/262-267) 
Shaykh al-Islam Ibn Taymiyah and his student Ibn al-Qayyim favoured the view that the pilgrim should not offer an udhiyah. (Al-Iqna' (1/409) and al-Insaf (4/110)
This view was also regarded as more correct by Shaykh Ibn ‘Uthaymin (may Allah have mercy on him). He (may Allah have mercy on him) was asked: How can a person combine udhiyah and Hajj, and is that prescribed? 
He replied: 
“The pilgrim does not offer an udhiyah, rather he offers a hadiy. Hence the Prophet (peace and blessings of Allah be upon him) did not offer an udhiyah during the Farewell Hajj, rather he offered a hadiy. But if we assume that he is doing Hajj by himself and his family are in his homeland, then in that case he should leave his family enough money to buy an animal and offer it as an udhiyah, so he will be offering a hadiy and they will be offering an udhiyah, because the udhiyah is only prescribed in places other than Makkah, but in Makkah it should be a hadiy.” (Al-Liqa al-Shahri) 
And Allah knows best.