In this paper an optimization model is presented for the synthesis of a heat exchanger network (HEN) for multiperiod operations. A literature very well-known stagewise superstructure is used, but isothermal mixing assumption is not made and a timesharing procedure is adopted. A MINLP problem is solved separately for each period of operation. The final multiperiod HEN is synthesized automatically considering the greatest areas and not fixing matches in each device in different periods, which avoids excessive heat exchange areas. Heat exchangers are designed to be feasible in practice, with a minimum acceptable area. Three literature problems were used to test the applicability of the proposed model. The objective function aims to minimize the total annualized cost (TAC). During implementation of the model, inconsistencies found in the literature were corrected. Results indicate that lower TACs were obtained in the present paper and each heat transfer device is feasible in practice.