Distance Constrained Facility Location Problem

The distance constrained facility location problem (DCFLP) seeks to the optimal way of locating facilities to minimize total costs (opening costs plus routing costs), while satisfying all the clients could be serviced by facilities within given distance. The paper first proposes a mixed 0-1 integer programming model for the DCFLP. Then, we present a ln(n)+1 approximation algorithm to solve the problem. We also extend the model and algorithm to the distance constrained hub location problem which obtains a 2ln(n)+1-approximation algorithm.