Abstract: In the k-level uncapacitated facility location problem, we are
given a set of clients and a set of facilities each having a specified
level. Each client has to be serviced by a sequence/path of k different
facilities, one from each level. There is a positive fixed cost for
setting up a facility, and a per unit cost of shipping goods between
each pair of locations. The distances are all non-negative and satisfy
the triangle inequality. We look for a solution with minimal cost where
all demands of the clients are met.
A 3-approximation algorithm is presented.