Find matching couples to maximize global happiness

Question

A belated Valentines day question for you all:

Suppose we have M men an W women, and they are all heterosexual. We have a (MxW) matrix A where A[m, w] quantifies how happy the couple (m, w) would be if married.

How can we pair the couples so that the global maximum happiness is achieved? (ie I'm looking to produce a length min(M, W) array of 2-tuples identifying who should be paired up, such that sum(A[m, w] for m, w in couples) is maximized, and each m and each w is only used once.

Note 1: Ideally I'm looking for a fast numpy implementation, but that's kind of secondary to finding the right algorithm.
Note 2: This is similar, but not the same as the Stable Marriage Problem , where you specify each person's ranked preferences instead of a happiness value.

Answer 1

Well, thanks to the commenters for pointing out that this is the Assignment Problem , and is usually described in terms of workers and jobs.

Scipy has a function that solves it using the Hungarian Algorithm.