I have enough money to perform hajj but I am physically incapable of undertaking it. Is it permissible to commission someone to make hajj on my behalf?

Abdullah Ibn 'Abbas [may Allah be pleased with them both] said, "Al-Fadl Ibn 'Abbas was riding behind the Prophet when a woman from Khath'am came up to him and said, "O, Messenger of Allah! My father is an old man. He cannot sit firmly on his mount and therefore cannot perform the obligation of hajj. May I perform it on his behalf?" "Yes," the Prophet answered. This was during the Farewell Pilgrimage.[1]

The ruling
A person who is incapable of riding (due to old age or chronic illness) is known in Islamic law as ma'dub. Based on this, it is permissible to commission another to perform hajj on your behalf.
Allah the Almighty knows best.

[1]Reported by Bukhari and Muslim