What is the permissibility of paying part of zakat in the form of foodstuffs needed by any household such as rice, sugar oil and the like?

The principle is that zakat be paid from the same type of goods on which it is due.
When the Prophet [pbuh] sent Mu'adh to Yemen, he told him, "Take grains from grains, sheep from sheep, camels from camels, and cows from cows" [Reported by Abu Dawud, ibn Majah and al Hakim who declared it authentic].

Hanafi scholars and others maintained the permissibility of paying an equivalent value from wealth other than the same kinds of goods upon which it is due. This is because the original restriction was meant only to facilitate its payment (from goods he already possessed) and not because it is in itself obligatory.

They based their opinion on Tawus' report in which he said, "Mu`adh (may Allah be pleased with him) told the people of Yemen, 'Bring me fabric and garments as zakat instead of barley and corn; this is easier for you and better for the Companions of the Prophet in Medina" [Reported by Bukhari and Bayhaqi]. Imam Al-Shafi'i said that even though Tawus did not meet Mu`adh, he knew that Mu'adh understood the Prophet's order in light of the general benefit inasmuch as this facilitated matters for the zakat givers. He therefore refrained from accepting zakat from the same kind of goods possessed by the zakat giver when he realized that the benefit of the people lay elsewhere. This was because the people of Yemen were famous for their textile industry and thus it was easier for them to pay their zakat from the merchandise they produced and because these fabrics were needed by the people of Medina.

Umar ibn al-Khatab (may Allah be pleased with him) used to do the same. Sa'id ibn Mansur reported in his Sunan that `Atta said, "Umar ibn al-Khattab used to take trade goods as zakat instead of dirhams [money]."

This is the opinion we prefer, since the ultimate objective of zakat is to fulfill the needs of the poor and the needy. As long as the kinds of goods paid as zakat fulfill the needs of the poor and are beneficial to them, they fulfill the objective of zakat.

The Ruling

It is permissible to pay part of one's zakat in the form of foodstuff that suit the needs of the poor and the destitute.

Allah Almighty knows best.