(i) For any input instance of \J with $d$ jobs, the makespan of an
optimum schedule is at most $ m+ o(m)$, for $d = o(m^{1/2})$.
For $d = o(m^{1/2})$, this improves on the upper bound $O(m + d)$
given in \cite{LMR99} with a constant equal to two as shown in
\cite{S98}. For $d=2$ the upper bound is improved to $m +
\lceil \; \sqrt{m} \; \rceil$.

(ii) There exist input instances of \J with $d = 2$ such that the
makespan of an optimum schedule is at least $m+\lceil \; \sqrt{m} \; \rceil$, i.e., the
result (i) cannot be improved for $d=2$.

(iii) We present a randomized on-line approximation
algorithm for \J with the best known approximation ratio for
$d = o(m^{1/2})$.

(iv) A deterministic approximation algorithm for \J is described
that works in quadratic time for constant $d$ and has an
approximation ratio of $1 + 2^d/\lfloor \sqrt{m} \, \rfloor$.