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Given two sets A={a_1,a_2,...,a_s} and {b_1,b_2,...,b_t}, a many-to-manymatching with demands and capacities (MMDC) between A and B matches eachelement a_i in A to at least \alpha_i and at most \alpha'_i elements in B, andeach element b_j in B to at least \beta_j and at most \beta'_j elements in Afor all 1=<i<=s and 1=<j<=t. In this paper, we present an algorithm for findinga minimum-cost MMDC between A and B using the well-known Hungarian algorithm.

Computing a many-to-many matching with demands and capacities between two sets using the Hungarian algorithm