  The main focus of this paper is radius-based (supplier) clustering in the
two-stage stochastic setting with recourse, where the inherent stochasticity of
the model comes in the form of a budget constraint. In addition to the standard
(homogeneous) setting where all clients must be within a distance $R$ of the
nearest facility, we provide results for the more general problem where the
radius demands may be inhomogeneous (i.e., different for each client). We also
explore a number of variants where additional constraints are imposed on the
first-stage decisions, specifically matroid and multi-knapsack constraints, and
provide results for these settings.
  We derive results for the most general distributional setting, where there is
only black-box access to the underlying distribution. To accomplish this, we
first develop algorithms for the polynomial scenarios setting; we then employ a
novel scenario-discarding variant of the standard Sample Average Approximation
(SAA) method, which crucially exploits properties of the restricted-case
algorithms. We note that the scenario-discarding modification to the SAA method
is necessary in order to optimize over the radius.
