  Bin packing is a well studied problem involved in many applications. The
classical bin packing problem is about minimising the number of bins and
ignores how the bins are utilised. We focus in this paper, on a variant of bin
packing that is at the heart of efficient management of data centres. In this
context, servers can be viewed as bins and virtual machines as items. The
efficient management of a data-centre involves minimising energy costs while
ensuring service quality. The assignment of virtual machines on servers and how
these servers are utilised has a huge impact on the energy consumption. We
focus on a bin packing problem where linear costs are associated to the use of
bins to model the energy consumption. We study lower bounds based on Linear
Programming and extend the bin packing global constraint with cost information.
