A local search approximation algorithm for the uniform capacitated k-facility location problem

In the uniform capacitated k-facility location problem (UC-k-FLP), we are given a set of facilities and a set of clients. Every client has a demand. Every facility have an opening cost and an uniform capacity. For each client–facility pair, there is an unit service cost to serve the client with unit demand by the facility. The total demands served by a facility cannot exceed the uniform capacity. We want to open at most k facilities to serve all the demands of the clients without violating the capacity constraint such that the total opening and serving cost is minimized. The main contribution of this work is to present the first combinatorial bi-criteria approximation algorithm for the UC-k-FLP by violating the cardinality constraint.