Drilling new oil fields in Alaska

This article says that the government has allowed for the first drilling to take place in the national petroleum reserve in Alaska. This will allow the United States to increase our production of oil which is the primary source of fuel to power various types of machinery. The question that I have is if this will have any effect on the price of a barrel of oil (or gallon of gas). Drilling for this oil should increase the supply of oil in the world but I am wondering by how much and if it will be significant enough to lower the price of crude since so much is already produced.