  In this paper, we study the hard uniform capacitated $k$- median problem
using local search heuristic. Obtaining a constant factor approximation for the
\ckm problem is open. All the existing solutions giving constant-factor
approximation, violate at least one of the cardinality and the capacity
constraints. All except Koruplou et al are based on LP-relaxation.
  We give $(3+\epsilon)$ factor approximation algorithm for the problem
violating the cardinality by a factor of $8/3 \approx 2.67$. There is a
trade-off between the approximation factor and the cardinality violation
between our work and the existing work. Koruplou et al gave $(1 + \alpha)$
approximation factor with $(5 + 5/\alpha)$ factor loss in cardinality using
local search paradigm. Though the approximation factor can be made arbitrarily
small, cardinality loss is at least $5$.
  On the other hand, we improve upon the results in
[capkmGijswijtL2013],[capkmshili2014], [Lisoda2016] in terms of factor-loss
though the cardinality loss is more in our case. Also, these results are
obtained using LP-rounding, some of them being strengthened, whereas local
search techniques are simple to apply and have been shown to perform well in
practice via empirical studies.
  We extend the result to hard uniform capacitated $k$-median with penalties.
To the best of our knowledge, ours is the first result for the problem.
