  Specifying a proper input distribution is often a challenging task in
simulation modeling. In practice, there may be multiple plausible distributions
that can fit the input data reasonably well, especially when the data volume is
not large. In this paper, we consider the problem of selecting the best from a
finite set of simulated alternatives, in the presence of such input
uncertainty. We model such uncertainty by an ambiguity set consisting of a
finite number of plausible input distributions, and aim to select the
alternative with the best worst-case mean performance over the ambiguity set.
We refer to this problem as robust selection of the best (RSB). To solve the
RSB problem, we develop a two-stage selection procedure and a sequential
selection procedure; we then prove that both procedures can achieve at least a
user-specified probability of correct selection under mild conditions.
Extensive numerical experiments are conducted to investigate the computational
efficiency of the two procedures. Finally, we apply the RSB approach to study a
queueing system's staffing problem using synthetic data and an
appointment-scheduling problem using real data from a large hospital in China.
We find that the RSB approach can generate decisions significantly better than
other widely used approaches.
