  This research considers the ranking and selection with input uncertainty. The
objective is to maximize the posterior probability of correctly selecting the
best alternative under a fixed simulation budget, where each alternative is
measured by its worst-case performance. We formulate the dynamic simulation
budget allocation decision problem as a stochastic control problem under a
Bayesian framework. Following the approximate dynamic programming theory, we
derive a one-step-ahead dynamic optimal budget allocation policy and prove that
this policy achieves consistency and asymptotic optimality. Numerical
experiments demonstrate that the proposed procedure can significantly improve
performance.
