The use of simulation as an engineering tool to design complex compute
r stochastic systems is often inhibited by cost. Extensive computer pr
ocessing is needed to recompute performance functions for changes in i
nput parameters. Moreover, simulation models are often subject to erro
rs caused by the input data in estimating the parameters of the input
distributions. The 'what if' analysis is needed to establish confidenc
e in a model's validity with respect to small changes in the system's
parameters. To solve the 'what if' problem for several scenarios requi
res a separate simulation run for each scenario. A method to estimate
the performance for several scenarios using a single simulation run ba
sed on the efficient score function is developed. The approximate func
tion is an exponential random function which is tangential to the perf
ormance function in expectation. We study the algorithm's properties a
nd examine the validity of the estimates based on this single run proc
edure by performing some experimental studies on some simple queueing
and pert models. Implementation 'details' necessary to package this me
thod with existing simulation software are provided. Finally, there is
a set of recommended directions for future research.