  We consider the classical problem of scheduling $n$ jobs with release dates
on both single and identical parallel machines. We measure the quality of
service provided to each job by its stretch, which is defined as the ratio of
its response time to processing time. Our objective is to schedule these jobs
non-preemptively so as to minimize sum stretch. So far, there have been very
few results for sum stretch minimization especially for the non-preemptive
case. For the preemptive version, the Shortest remaining processing time (SRPT)
algorithm is known to give $2$-competitive for sum stretch on single machine
while its is $13$-competitive on identical parallel machines. Leonardi and
Kellerer provided the strong lower bound for the more general problem of
\textit{sum (weighted) flow time} in single machine and identical parallel
machines, respectively . Therefore, we study this problem with some additional
assumptions and present two new competitive ratio for existing algorithms. We
show that the Shortest processing time (SPT) algorithm is $\Delta -
\frac{1}{\Delta}+1$-competitive for non-preemptive sum stretch minimization on
single machine and it is $\Delta - \frac{1}{\Delta}+ \frac{3}{2} -\frac{1}{2m}$
on $m$ identical parallel machines, where $\Delta$ is the upper bound on the
ratio between the maximum and the minimum processing time of the jobs.
