i work at an apple authorized service center (that also is a partner with IBM/Lenovo, HP, and Sony) and we get overnighted parts directly from the company (apple, ibm, lenovo, cisco, whatever) whenever we do a warranty claim.
all warranty work is free also. the customers pay nothing, and its done in 1-5 business days. anything beyond that and our ratings go down and we make less money.
1 month....we would be charged for the part and not paid for the labor if we did that shit. there is no excuse for the turn around time you or whoever experienced.