Abstract
We consider the k-level facility location problem with soft capacities (k-LFLPSC). In the k-LFLPSC, each facility i has a soft capacity u i along with an initial opening cost f i ≥ 0, i.e., the capacity of facility i is an integer multiple of u i incurring a cost equals to the corresponding multiple of f i . We firstly propose a new bifactor (ln(1/β)/(1 −β),1+2/(1 −β))-approximation algorithm for the k-level facility location problem (k-LFLP), where β ∈ (0, 1) is a fixed constant. Then, we give a reduction from the k-LFLPSC to the k-LFLP. The reduction together with the above bifactor approximation algorithm for the k-LFLP imply a 5.5053-approximation algorithm for the k-LFLPSC which improves the previous 6-approximation.
Published Version
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