  Speed-robust scheduling is the following two-stage problem of scheduling $n$
jobs on $m$ uniformly related machines. In the first stage, the algorithm
receives the value of $m$ and the processing times of $n$ jobs; it has to
partition the jobs into $b$ groups called bags. In the second stage, the
machine speeds are revealed and the bags are assigned to the machines, i.e.,
the algorithm produces a schedule where all the jobs in the same bag are
assigned to the same machine. The objective is to minimize the makespan (the
length of the schedule). The algorithm is compared to the optimal schedule and
it is called $\rho$-robust, if its makespan is always at most $\rho$ times the
optimal one.
  Our main result is an improved bound for equal-size jobs for $b=m$. We give
an upper bound of $1.6$. This improves previous bound of $1.8$ and it is almost
tight in the light of previous lower bound of $1.58$. Second, for
infinitesimally small jobs, we give tight upper and lower bounds for the case
when $b\geq m$. This generalizes and simplifies the previous bounds for $b=m$.
Finally, we introduce a new special case with relatively small jobs for which
we give an algorithm whose robustness is close to that of infinitesimal jobs
and thus gives better than $2$-robust for a large class of inputs.
