  Power consumption is the major cost factor in data centers. It can be reduced
by dynamically right-sizing the data center according to the currently arriving
jobs. If there is a long period with low load, servers can be powered down to
save energy. For identical machines, the problem has already been solved
optimally by Lin et al. (2013) and Albers and Quedenfeld (2018).
  In this paper, we study how a data-center with heterogeneous servers can
dynamically be right-sized to minimize the energy consumption. There are $d$
different server types with various operating and switching costs. We present a
deterministic online algorithm that achieves a competitive ratio of $2d$ as
well as a randomized version that is $1.58d$-competitive. Furthermore, we show
that there is no deterministic online algorithm that attains a competitive
ratio smaller than $2d$. Hence our deterministic algorithm is optimal. In
contrast to related problems like convex body chasing and convex function
chasing, we investigate the discrete setting where the number of active servers
must be integral, so we gain truly feasible solutions.
