In this paper, we seek to design a Groves mechanism for
assigning p heterogeneous objects among n competing agents (n > p)
with unit demand, satisfying weak budget balance, individual rational-
ity, and minimizing the budget imbalance. This calls for designing an
appropriate rebate function. When the objects are identical, this prob-
lem has been solved by Moulin [1] and Guo and Conitzer [2]. However, it
remains an open problem to design such a rebate function when the ob-
jects are heterogeneous. We propose a mechanism, HETERO and conjec-
ture that HETERO is individually rational and weakly budget balanced.
We provide empirical evidence for our conjecture through experimental
simulations.