  Motivated by settings such as medical treatments or aircraft maintenance, we
consider a scheduling problem with jobs that consist of two operations, a test
and a processing part. The time required to execute the test is known in
advance while the time required to execute the processing part becomes known
only upon completion of the test. We use competitive analysis to study
algorithms for minimizing the sum of completion times for $n$ given jobs on a
single machine. As our main result, we prove using a novel analysis technique
that the natural $1$-SORT algorithm has competitive ratio at most 1.861. For
the special case of uniform test times, we show that a simple threshold-based
algorithm has competitive ratio at most 1.585. We also prove a lower bound that
shows that no deterministic algorithm can be better than $\sqrt{2}$-competitive
even in the case of uniform test times.
