  We present an algorithm to compute the rank of a configuration of the
sandpile model for the complete bipartite graph K_{m,n} of complexity O(m+n).
Furthermore, we provide a formula for the generating function of parking sorted
configurations on complete bipartite graphs K_{m,n} according to rank, degree,
and the sizes m and n.
  The results in the present paper are similar to those found by Robert Cori
and the second named author for the complete graph K_{n+1}, and they rely on
the analysis of certain operators on the stable sorted configurations of
K_{m,n} developed in a previous work by the authors together with
Jean-Christophe Aval and Mark Dukes.
