Before revision: Given two point sets S and T, we first study the many-to-many matching with demands problem (MMDproblem) where each point of one set must be matched to  a given number of the points of the other set.
After revision: Given two point sets S and T, we first study the many-to-many matching with demands problem (MMDproblem) where each point of one set must be matched to at least a given number of the points of the other set.