  We first show that a better analysis of the algorithm for The Two-Sage
Stochastic Facility Location Problem from Srinivasan \cite{sri07} and the
algorithm for The Robust Fault Tolerant Facility Location Problem from Byrka et
al \cite{bgs10} can render improved approximation factors of 2.206 and \alpha+4
where \alpha is the maximum number an adversary can close, respectively, and
which are the best ratios so far.
  We then present new models for the soft-capacitated facility location problem
with uncertainty and design constant factor approximation algorithms to solve
them. We devise the stochastic and robust approaches to handle the uncertainty
incorporated into the original model. Explicitly, in this paper we propose two
new problem, named The 2-Stage Soft-Capacitated Facility Location Problem and
The Robust Soft-Capacitated Facility Location Problem respectively, and present
constant factor approximation algorithms for them both. Our method uses
reductions between facility location problems and linear-cost models, the
randomized thresholding technique of Srinivasan \cite{sri07} and the filtering
and clustering technique of Byrka et al \cite{bgs10}.
