The soft-capacitated facility location problem, where each facility is composed of a variable number of fixed-capacity production units, has been recently studied in several papers, especially in the metric case. 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 subproblem is approximately solved by a fully polynomial-time approximation scheme based on cost scaling and dynamic programming, achieves a logaritmic approximation ratio of (1 + ε)H(n) for the problem, where n is the number of customers to be served and H is the harmonic series. This improves the previous bound of 2H(n) for this problem.
