  We consider several extensions of the fractional bin packing problem, a
relaxation of the traditional bin packing problem where the objects may be
split across multiple bins. In these extensions, we introduce load-balancing
constraints imposing that the share of each object which is assigned to a same
bin must be equal. We propose a Mixed-Integer Programming (MIP) formulation and
show that the problem becomes NP-hard if we limit to at most 3 the number of
bins across which each object can be split.
  We then consider a variant where the balanced allocations of objects to bins
may be done in successive rounds; this problem was inspired by
telecommunication applications, and may be used to model simple Live Streaming
networks. We show that two rounds are always sufficient to completely assign
all objects to the bins and then provide an optimal polynomial-time allocation
algorithm for this problem.
