CPR SMT WRONG RWY APCH.

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CORPORATE BUSINESS FLT FROM BOS TO DTW. WE WERE HANDED OFF FROM CLE CENTER TO DTW APCH CTL. WE WERE ASSIGNED A HDG TO MAINTAIN; AN ALT; AND TOLD TO EXPECT RADAR VECTORS FOR AN ILS 3L APCH. EVERYTHING SEEMED NORMAL UNTIL WE WERE GIVEN THE FINAL HDG TO 'INTERCEPT THE LOC; MAINTAIN 2700' UNTIL ESTABLISHED ON APCH; CONTACT TWR ON 118.4.' THERE IS NO 2700' DEPICTED ON THE ILS 3L APCH. 118.4 IS THE TWR FREQ FOR THE RIGHT SIDE OF THE ARPT. WE DID NOT INTERCEPT THE LOC IN A NORMAL AMOUNT OF TIME. I ASKED THE TWR IF THEY SHOWED US TO THE RIGHT OF COURSE. THEIR RESPONSE WAS: 'NO; WE SHOW YOU TO THE LEFT OF COURSE; TURN RIGHT TO A HDG OF 050 DEGS.' I THEN ASKED THE TWR TO 'CONFIRM WE ARE CLRED FOR THE ILS 3L?' 'NO; YOU WERE CLRED FOR THE ILS TO RWY 3R; EXECUTE MISSED APCH ACFT 3 MI BEHIND YOU.' WHAT WENT WRONG? WE PLANNED AN APCH TO THE LEFT RWY BUT AT SOME POINT IN TIME WERE CHANGED TO THE RIGHT RWY. WE WERE NOT MADE AWARE OF THIS CHANGE NOR DID WE ACKNOWLEDGE IT. THIS TYPE OF SIDESTEP IS NORMAL HERE IN DTW AND BENEFICIAL TO THE AIRLINES AND GA AS WELL. WE BOTH LAND NEAR TO OUR GATE AREAS. CORRECTIVE ACTION: I THINK THE REAL PROBLEM IS THE WORKLOAD OF APCH CTL RADAR. THEIR STAFF LEVEL MUST BE INCREASED. ACR X AIRLINES WAS MERGED WITH ACR Y AIRLINES. ACR X IN TURN; MADE DTW A MAJOR HUB. THIS SIGNIFICANTLY INCREASED ALL OPS. ANY ARPT WITH PARALLEL RWYS SHOULD HAVE DIFFERENT RWY NUMBERS FOR INSTRUMENT RWY APCHS. FOR EXAMPLE; ATL. ATL'S RWY 8 AND RWY 9 ARE IN FACT PARALLEL. REQUIRE MORE TIMES BEING TOLD EXACTLY WHAT INSTRUMENT APCH YOU ARE BEING VECTORED FOR AND THE ACKNOWLEDGEMENTS AS WELL.