The decision version of the MINIMUM MULTISETS BINDING (MMB) problem was discussed and proved to be NP-complete in [1]. In this paper, we will prove that there is no polynomial time algorithm with constant difference guarantee, no fully polynomial approximation scheme and no polyllomial approximation scheme for the optimization version of the MMB problem unless P = NP. An approximation algorithm called SM which takes polynomial time is then provided to achieve the ahsolute performance ration 
for any instance I of the MMB problem, where n is the "length" of the instance I.