# Reducing resource allocation problem to bipartite matching

There are a set of bins, $B$ and a set of resources $R$. Each $b \in B$ is associated with a set function $Z_b(S) : 2^R \rightarrow \mathbb{R}^+$. The resource allocation problem is to find a partition of $R$, $\{R_b : b\in B\}$ that maximizes $\sum_{b \in B} Z_b(R_b)$. This problem is NP-hard if no constraints are imposed on $Z_b$. Is there any way to reduce this to finding the maximum-weight matching over some bipartite graph? Of course the number of left/right nodes would have to be exponential in number since bipartite matching is solvable in poly-time.