Improved Approximation of the General Soft-Capacitated Facility Location Problem

An NP-hard variant of the single-source Capacitated Facility Location Problem is studied, where each facility is composed of a variable number of fixed-capacity production units. This problem, especially the metric case, has been recently studied in several papers. In this paper, we only consider the general problem where connection costs do not systematically satisfy the triangle inequality property. We show that an adaptation of the set covering greedy heuristic, where the sub-problem is approximately solved by a Fully Polynomial-Time Approximation Scheme based on cost scaling and dynamic programming, achieves a logarithmic approximation ratio of (1+ƒÕ)H(n) for the problem, where n is the number of clients to be served, and H is the harmonic series. This improves the previous bound of 2H(n) for this problem.