Most dogs if you yell at them to stop barking, they just think you are joining in the barking and it validates their decision to bark. Therefore the behavior doesn't go away.
For me, I would absolutely not let this dog in for barking. He can stay outside and learn to be quite. I also might make sure I praise him for not barking at the door and let him in prior to barking. Also, you can teach him to bark once and then be quite. Just reward after the first alert to come in by letting him in after the first bark (if you like the bark to tell you he wants back in). It's going to require you being there watching and waiting while he's out. Your timing is key here. Some people have used a bell on the door and had their dog ring that as a substitute behavior to the barking to let them know.
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Chelle and the rest of the crew including, but not limited to Kita and Taiko (the shiba inu wrestle maniacs), Adi (reserved and dignified tabby cat), and all 28 reptiles