Multi-objective optimization is an optimization problem with some conflicting objectives to be attained, simultanously. This paper reviewed literature about multi-objective optimization problems for supply chain management. The review aimed to provide the lastest research views and recomendations for further studies. We discussed the lastest ten years publications about multi-objective optimization for supply chain management. The scope of this review was classified into five categories i.e. problem statements, multi-objective frameworks, mathematical formulation modeling, optimization techniques, and representation of supply chain. Multi-objective optimization approaches, both classical and metaheuristic approaches, were discussed, accordingly. In this review, we conducted conclusion and recomendations about likelihood research directions in future.