  We present a first study on the energy required to reduce a unit mass
fragment by consecutively using several devices, as it happens in the mining
industry. Two devices are considered, which we represent as different
stochastic fragmentation processes. Following the self-similar energy model
introduced by Bertoin and Martinez, we compute the average energy required to
attain a size x with this two-device procedure. We then asymptotically compare,
as x goes to 0 or 1, its energy requirement with that of individual
fragmentation processes. In particular, we show that for certain range of
parameters of the fragmentation processes and of their energy cost-functions,
the consecutive use of two devices can be asymptotically more efficient than
using each of them separately, or conversely.
