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This paper addresses the two-stage production problem with parallel machines. We present two mathematical models that consider the production of different products with two stages of production in parallel machines and buffer between the stages. The two models consider minimum and maximum time of permanence of the items in the buffer, and the second considers costs of discarding, reprocessing and acceleration of the lots. Also, we propose several strategies of Fix and Optimize heuristic that start from an initial solution, through a constructive heuristic of decomposition. In general, the results show that the heuristic strategies can achieve competitive solutions in short computational time, outperforming the results provided by the optimization solver. [ABSTRACT FROM AUTHOR]