  With growing emphasis on e-commerce marketplace platforms where we have a
central platform mediating between the seller and the buyer, it becomes
important to keep a check on the availability and profitability of the central
store. A store serving too less clients can be non-profitable and a store
getting too many orders can lead to bad service to the customers which can be
detrimental for the business. In this paper, we study the facility location
problem(FL) with upper and lower bounds on the number of clients an open
facility serves. Constant factor approximations are known for the restricted
variants of the problem with only the upper bounds or only the lower bounds.
The only work that deals with bounds on both the sides violates both the bounds
[8]. In this paper, we present the first (constant factor) approximation for
the problem violating the upper bound by a factor of (5/2) without violating
the lower bounds when both the lower and the upper bounds are uniform. We first
give a tri-criteria (constant factor) approximation violating both the upper
and the lower bounds and then get rid of violation in lower bounds by
transforming the problem instance to an instance of capacitated facility
location problem.
