I think you're over favouring. Fed this set:

10
1001 2002
1003 2002
1003 2005
1003 2005
1005 2002
1005 2002
1008 2002
1009 2005
1010 2002
1010 2002
[download]

Yours outputs:

3
1009
2002
1003
[download]

where this is possible and (to my interpretation of the rules) therefore better:

2
2002
2005
[download]

Mine's broken in the reverse way in that it ignores (actually, doesn't even consider), equally valid solutions that would use the favoured employee.