The fault-tolerant facility allocation problem

We study the problem of Fault-Tolerant Facility Allocation (FTFA) which is a relaxation of the classical Fault-Tolerant Facility Location (FTFL) problem [1]. Given a set of sites, a set of cities, and corresponding facility operating cost at each site as well as connection cost for each site-city pair, FTFA requires to allocate each site a proper number of facilities and further each city a prespecified number of facilities to access. The objective is to find such an allocation that minimizes the total combined cost for facility operating and service accessing. In comparison with the FTFL problem which restricts each site to at most one facility, the FTFA problem is less constrained and therefore incurs less cost which is desirable in application. In this paper, we consider the metric FTFA problem where the given connection costs satisfy triangle inequality and we present a polynomial-time algorithm with approximation factor 1.861 which is better than the best known approximation factor 2.076 for the metric FTFL problem [2].