  There is a long history of approximation schemes for the problem of
scheduling jobs on identical machines to minimize the makespan. Such a scheme
grants a $(1+\epsilon)$-approximation solution for every $\epsilon > 0$, but
the running time grows exponentially in $1/\epsilon$. For a long time, these
schemes seemed like a purely theoretical concept. Even solving instances for
moderate values of $\epsilon$ seemed completely illusional. In an effort to
bridge theory and practice, we refine recent ILP techniques to develop the
fastest known approximation scheme for this problem. An implementation of this
algorithm reaches values of $\epsilon$ lower than $2/11\approx 18.2\%$ within a
reasonable timespan. This is the approximation guarantee of MULTIFIT, which, to
the best of our knowledge, has the best proven guarantee of any non-scheme
algorithm.
