I want to organize $2n$ people ${A, B, C, \dots}$ in pairs. Each people rates every other one with an integer number going from 0 to 10. The ratings may not be reciprocal (i.e., A may rate B a 10, and B rates A a 3). Ratings are given as a matrix. Here is an example :
A B C D
---------
A 0 6 10
B 3 7 2
C 3 9 4
D 7 8 4
I want to find a matching that maximizes : variant a) the sum of the rating in couples. variant b) the minimum of the ratings in couples.
With the matrix above, if I match A with B and C with D, I have a score of 11 with variant (a), and 0 with variant (b).
This looks like a simpler case of stable roommate problem. Is this variant NP-hard?