This code should work. It creates a hash, the part number being the key. The value is another hash, containing two keys, num and des, whose values are the quantity and the list of designators.

#!/usr/bin/perl

use strict;
use warnings;

my %parts;

while(my $line = <DATA>){
  chomp $line;
  $line =~ s/"//g;
  my ($part,$num,@des) = split /,/,$line;
  $parts{$part}{num} += $num;
  $parts{$part}{des} = {} unless exists $parts{$part}{des};
  my %des = %{ $parts{$part}{des} };
  @des{@des} = ();
  %{ $parts{$part}{des} } = %des;
}
foreach my $part_id (sort keys %parts){
  my $part = $parts{$part_id};
  my $des_string = join ',', sort keys %{ $part->{des} };
  $des_string = '"'.$des_string.'"' if $des_string =~ /,/;
  print join ',',$part_id,$part->{num},$des_string;
  print "\n";
}

__DATA__
032-00751-0000,1,R383
032-00794-0000,6,"RP1,RP2,RP3,RP22,RP24,RP26"
032-00795-0000,8,"RP10,RP11,RP12,RP13,RP14,RP15,RP16,RP17"
032-00804-0000,7,"R7,R14,R21,R23,R41,R42,R49"
032-00807-0000,2,"RP18,RP19"
032-00807-0000,4,"RP8,RP9,RP200,RP201"
032-00808-0000,3,"RP21,RP23,RP25"
032-00820-0000,5,"R966,R970,R971,R1041,R1076"
032-00820-0000,1,R3000
032-00893-0000,1,R1164
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Update: designators sorted.