B34 Hardness of Approximating Transshipment Problems with Permutable Transit Vectors(Advanced machining technology)

Abstract

In this paper, we deal with the inapproximability of a transshipment problem with a permutable transit vector. We have already known that the transshipment problem is NP-hard in the strong sense. We prove in this paper that even if the shipping cost associated with every arc is given as a positive integer, there is no polynomial time constant factor approximation algorithm for the transshipment problem under the hypothesis that P≠NP. The inapproximability result is obtained by a gap-introducing reduction from an NP-complete problem 3DM.