  This paper studies a single-machine scheduling problem with a non-renewable
resource (NR-SSP) and total weighted completion time criterion. The
non-renewable resource is consumed when the machine starts processing a job. We
consider the case where each job's weight in the objective function is
proportional to its resource consumption amount. The problem is known to be
NP-hard in this case. We propose a 3-approximation list scheduling algorithm
for this problem. Besides, we show that the approximation ratio 3 is tight for
the algorithm.
