  In this paper, we give first constant factor approximation for capacitated
knapsack median problem (CKM) for hard uniform capacities, violating the budget
only by an additive factor of $f_{max}$ where $f_{max}$ is the maximum cost of
a facility opened by the optimal and violating capacities by $(2+\epsilon)$
factor. Natural LP for the problem is known to have an unbounded integrality
gap when any one of the two constraints is allowed to be violated by a factor
less than $2$. Thus, we present a result which is very close to the best
achievable from the natural LP. To the best of our knowledge, the problem has
not been studied earlier.
  For capacitated facility location problem with uniform capacities, a constant
factor approximation algorithm is presented violating the capacities a little
($1 + \epsilon$). Though constant factor results are known for the problem
without violating the capacities, the result is interesting as it is obtained
by rounding the solution to the natural LP, which is known to have an unbounded
integrality gap without violating the capacities. Thus, we achieve the best
possible from the natural LP for the problem. The result shows that natural LP
is not too bad.
  Finally, we raise some issues with the proofs of the results presented in
\cite{capkmByrkaFRS2013} for capacitated $k$-facility location problem
(C$k$FLP). \cite{capkmByrkaFRS2013} presents $O(1/\epsilon^2)$ approximation
violating the capacities by a factor of $(2 + \epsilon)$ using dependent
rounding. We first fix these issues using our techniques. Also, it can be
argued that (deterministic) pipage rounding cannot be used to open the
facilities instead of dependent rounding. Our techniques for CKM provide a
constant factor approximation for CkFLP violating the capacities by $(2 +
\epsilon)$.
