On the Integrality Gap of Capacitated Facility LocationZo

We consider the facility location problem with hard non-uniform upper and lower bounds on the amount of demand that can be routed to any facility. We examine the natural integer programming formulation of this problem. First, for the version with just the upper bounds (i.e., with the lower bounds being zero), we show that for every constant factor blowup in capacities, the integrality gap of the LP relaxation is a constant. We present a smooth trade-oo for the cost versus the blowup in capacities. Secondly, we show how to incorporate lower bounds into any approximation algorithm for the version with just the upper bounds. Non-uniform capacities make the problem signiicantly more diicult than the case involving uniform capacities.