The correct answer is option 3 - Indian Ordnance Factory Board. The Government of India has approved the production of 18 indigenous `Dhanush` artillery guns to be produced in India. The responsibility for producing these guns has been given to the Indian Ordnance Factory Board.

Option 1 - Indian Army is incorrect because the Indian Army is the end user of these artillery guns, not the producer. The Indian Army will acquire and operate these guns once they are produced.

Option 2 - US Army is also incorrect because the production of `Dhanush` artillery guns is a domestic project of the Indian government. There is no involvement of the US Army in the production process.

Option 4 - Indian and US Army jointly is incorrect because there is no collaboration between the Indian and US Army for the production of these artillery guns. The Indian Ordnance Factory Board is solely responsible for the production.

Therefore, the correct answer is option 3 - Indian Ordnance Factory Board.