  A method for computing the multigraded Hilbert depth of a module was
presented in [16]. In this paper we improve the method and we introduce an
effective algorithm for performing the computations. In a particular case, the
algorithm may also be easily adapted for computing the Stanley depth of the
module. We further present interesting examples which were found with the help
of an experimental implementation of the algorithm. Thus, we completely solve
several open problems proposed by Herzog in [12].
