  Semi-online models where decisions may be revoked in a limited way have been
studied extensively in the last years.
  This is motivated by the fact that the pure online model is often too
restrictive to model real-world applications, where some changes might be
allowed. A well-studied measure of the amount of decisions that can be revoked
is the migration factor $\beta$: When an object $o$ of size $s(o)$ arrives, the
decisions for objects of total size at most $\beta\cdot s(o)$ may be revoked.
Usually $\beta$ should be a constant. This means that a small object only leads
to small changes. This measure has been successfully investigated for
different, classic problems such as bin packing or makespan minimization. The
dual of makespan minimization - the Santa Claus or machine covering problem -
has also been studied, whereas the dual of bin packing - the bin covering
problem - has not been looked at from such a perspective.
  In this work, we extensively study the bin covering problem with migration in
different scenarios. We develop algorithms both for the static case - where
only insertions are allowed - and for the dynamic case, where items may also
depart. We also develop lower bounds for these scenarios both for amortized
migration and for worst-case migration showing that our algorithms have nearly
optimal migration factor and asymptotic competitive ratio (up to an arbitrary
small $\eps$). We therefore resolve the competitiveness of the bin covering
problem with migration.
