# Marriage problem

**DOI:**https://doi.org/10.1007/1-4020-0611-X_587

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Given a group of *m* men and *m* women, the marriage problem is to couple the men and women such that the “total happiness” of the group is maximized when the assigned couples marry. The women and the men determine an *m* × *m* table of happiness coefficients, where the coefficient *a*_{ij} represents the happiness rating for the couple formed by woman *i* and man *j* if they marry. The larger the *a*_{ij}, the higher the happiness. The problem can be formulated as an assignment problem whose solution matches each woman to one man. This result, which is due to the fact that the assignment problem has a solution in which the variables can take on only the values of 0 or 1, is sometimes used to “prove” that monogomy is the best form of marriage. Assignment problem.