  We seek to provide practicable approximations of the two-stage robust
stochastic optimization (RSO) model when its ambiguity set is constructed with
an f-divergence radius. These models are known to be numerically challenging to
various degrees, depending on the choice of the f-divergence function. The
numerical challenges are even more pronounced under mixed-integer first-stage
decisions. In this paper, we propose novel divergence functions that produce
practicable robust counterparts, while maintaining versatility in modeling
diverse ambiguity aversions. Our functions yield robust counterparts that have
comparable numerical difficulties to their nominal problems. We also propose
ways to use our divergences to mimic existing f-divergences without affecting
the practicability. We implement our models in a realistic location-allocation
model for humanitarian operations in Brazil. Our humanitarian model optimizes
an effectiveness-equity trade-off, defined with a new utility function and a
Gini mean difference coefficient. With the case study, we showcase 1) the
significant improvement in practicability of the RSO counterparts with our
proposed divergence functions compared to existing f-divergences, 2) the
greater equity of humanitarian response that our new objective function
enforces and 3) the greater robustness to variations in probability estimations
of the resulting plans when ambiguity is considered.
