When should the Haji offer his sacrifice?
Question

If a haji goes for hajj, is it waajib on him to do qurbani At his home place also ?
Praise be to Allah.1 – Hajj is of three types: Ifraad, Tamattu’ and Qiraan. 
Ifraad is when one does Hajj on its own (without ‘Umrah). Tamattu’ means doing ‘Umrah, then exiting the state of ihraam, then doing Hajj. Qiraan means doing Hajj and ‘Umrah together with one ihraam (only entering ihraam once for both), in which one Tawaaf and one Sa’ee is sufficient for both Hajj and ‘Umrah. 
It was narrated from ‘Urwah ibn al-Zubayr that ‘Aa’ishah (may Allah be pleased with her) said: “We set out with the Messenger of Allah SAWS (peace and blessings of Allah be upon him) shortly before the appearance of the new moon of Dhu’l-Hijjah and he said, ‘Whoever wants to assume ihraam for ‘Umrah may do so, and whoever wants to assume ihraam for Hajj may do so. Had I not brought the hadiy (sacrifice) with me, I would have assumed ihraam for ‘Umrah.’ Some of the people assumed ihraam for ‘Umrah and others for Hajj…”
(Narrated by al-Bukhaari, 1694; Muslim, 1211) 
2 – Ifraad means doing Hajj on its own, with no ‘Umrah beforehand. The one who is doing Ifraad does not have to offer a sacrifice, but it is mustahabb (recommended). 
3 – In the case of Tamattu’ and Qiraan, the sacrifice is obligatory. This is the blood of thanksgiving, by which the pilgrim thanks his Lord for prescribing this ritual for him. In Tamattu’ the pilgrim combines ‘Umrah and Hajj, exiting the state of ihraam in between, when he can enjoy (yatamatta’) wearing perfume and regular clothing, and having intercourse. 
It was narrated from Saalim ibn ‘Abd-Allah that Ibn ‘Umar (may Allah be pleased with them both) said: “During his last Pilgrimage, the Messenger of Allah SAWS (peace and blessings of Allah be upon him) did ‘Umrah and then Hajj. He drove a Hadiy (sacrificial animal) along with him from Dhu’l-Hulayfah. The Messenger of Allah SAWS (peace and blessings of Allah be upon him) started by assuming Ihram for 'Umrah, then for Hajj. And the people, too, assumed ihraam for ‘Umrah then for Hajj
along with the Prophet SAWS (peace and blessings of Allah be upon him). Some of them brought the Hadiy (sacrificial animals) and drove it along with them, whilst the others did not. So, when the Prophet SAWS (peace and blessings of Allah be upon him) reached Makkah, he said to the people, ‘Whoever among you has driven the Hadiy, should not finish his ihraam till he completes his Hajj. And whoever among you has not (driven) the Hadiy with him, should perform Tawaaf of the Ka'bah and the Tawaaf between Safa and Marwa, then cut short his hair and finish his ihraam, then  he should assume ihraam for Hajj. If anyone cannot afford a Hadiy, he should fast for three days during the Hajj and seven days when he returns home.”
(Narrated by al-Bukhaari, 1606, Muslim, 1227) 
4 – The hadiy (sacrifice) is that which the pilgrim gives as a gift (yahdeehi) to the Ancient House. It is one of the “al-an’aam” animals, i.e., sheep, cattle or camels, which he brings with him before entering ihraam. One of the differences between the one who does Tamattu’ and the one who does Qiraan is that the one who does Qiraan does not exit ihraam after finishing his ‘Umrah; he remains in ihraam until the eighth of Dhu’l-Hijjah, which is the day when he enters the intention for Hajj. 
The Sunnah is to slaughter the sacrifice on the day of Eid, which is the tenth of Dhu’l-Hijjah. 
It was narrated from Saalim ibn ‘Abd-Allah that Ibn ‘Umar (may Allah be pleased with them both) said: “During his last Pilgrimage, the Messenger of Allah SAWS (peace and blessings of Allah be upon him) performed ‘Umrah and then Hajj. He drove a Hadiy (sacrificial animal) along with him… then he went to Safa and Marwa and ran between them seven times and did not do any deed forbidden because of Ihraam, until he finished his Hajj and sacrificed his Hadiy on the day of Nahr (the tenth day of Dhul-Hijjah). He then hastened onwards (to Makkah) and performed Tawaaf of the Ka'bah, and then everything that was forbidden because of Ihraam became permissible.”
(Narrated by al-Bukhaari, 1606, Muslim, 1227) 
5 – No one among the pilgrims has to offer a sacrifice in his own country, because the sacrifice is one of the rituals (of Hajj), so it can only be done in Makkah. Even if the pilgrim has to offer a sacrifice because he did something which is not allowed during Hajj, he should not offer this sacrifice in his own country, rather it should be done in Mina or Makkah. 
‘Abd al-‘Azeem Aabaadi said: it is permissible to slaughter all the sacrificial animals in the sacred land (the Haram of Makkah), according to scholarly consensus, but Mina is the best place for offering the sacrifice of Hajj, and Makkah – except for al-Marwah – is the best place for offering the sacrifice of ‘Umrah. 
But if the pilgrim has a family whom he leaves behind in his own country and leaves with them money so that they can buy a sacrificial animal on the day of Eid, this is good. 
And Allah knows best.