Because the set of feasible subsets is generally exponentially large, finding the opti- mal subset is highly nontrivial. Brams and Potthoff (1998) were the first to discuss the computation of the Chamberlin-Courant and the Monroe voting schemes, showing that the optimal committee can be determined using integer programming. This provides a method that works in practice when the number of voters and items are small, but may not scale up well. They formulate an improved integer program for settings where the number of agents is large, but this modified integer program is still too large to be solved when the number of items is large