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In this paper, we give first constant factor approximation for capacitatedknapsack median problem (CKM) for hard uniform capacities, violating the budgetonly by an additive factor of $f_{max}$ where $f_{max}$ is the maximum cost ofa facility opened by the optimal and violating capacities by $(2+\epsilon)$factor. Natural LP for the problem is known to have an unbounded integralitygap when any one of the two constraints is allowed to be violated by a factorless than $2$. Thus, we present a result which is very close to the bestachievable from the natural LP. To the best of our knowledge, the problem hasnot been studied earlier.  For capacitated facility location problem with uniform capacities, a constantfactor approximation algorithm is presented violating the capacities a little($1 + \epsilon$). Though constant factor results are known for the problemwithout violating the capacities, the result is interesting as it is obtainedby rounding the solution to the natural LP, which is known to have an unboundedintegrality gap without violating the capacities. Thus, we achieve the bestpossible from the natural LP for the problem. The result shows that natural LPis 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 $O(1/\epsilon^2)$ approximationviolating the capacities by a factor of $(2 + \epsilon)$ using dependentrounding. We first fix these issues using our techniques. Also, it can beargued that (deterministic) pipage rounding cannot be used to open thefacilities instead of dependent rounding. Our techniques for CKM provide aconstant factor approximation for CkFLP violating the capacities by $(2 +\epsilon)$.

Constant factor Approximation Algorithms for Uniform Hard Capacitated Facility Location Problems: Natural LP is not too bad