  We consider online scheduling to minimize weighted completion time on related
machines, where each job consists of several tasks that can be concurrently
executed. A job gets completed when all its component tasks finish. We obtain
an $O(K^3 \log^2 K)$-competitive algorithm in the non-clairvoyant setting,
where $K$ denotes the number of distinct machine speeds. The analysis is based
on dual-fitting on a precedence-constrained LP relaxation that may be of
independent interest.
