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In this paper, we consider a multiperiod fuzzy production and sourcing problem that a manufacturer has a number of plants and/or subcontractors. The manufacturer has to meet the products demand according to the service level requirements set by its customers. Based on credibility theory, a new class of fuzzy production planning model is first proposed. Then we deal with the approximation of the fuzzy production planning problem with credibility service level constraints. After that, a hybrid algorithm, which integrates approximation approach and particle swarm optimization algorithm, is designed to solve the proposed production planning problem, and a numerical example is provided to test the effectiveness of the hybrid algorithm.