Supplier selection problem has a multicriteria nature. Sometimes several conflicting criteria with different importance must be considered in this decision, moreover, uncertainty is not avoidable in real cases. In this paper, a fuzzy non-linear multiobjective model is formulated in such a way to handle multicriteria and uncertain nature of supplier selection problem. The model consists of three objective functions that should be solved while satisfying the constraints of supplier's capacity and buyer's demand: 1) minimizing the total cost of logistics (including the net price, storage, transportation, and ordering costs), 2) maximizing the quality and 3) maximizing the service level. In order to solve the proposed model, a fuzzy weighted additive and mixed integer nonlinear programming is developed. The proposed model enables the decision maker to assign different fuzzy weight to various criteria. By assuming total cost of logistics as an objective function, multi-period inventory management issues are considered. A numerical example is developed to clarify how the model can be applied. Finally, the contributions and recommendations for future researches are discussed.