The interval based MINLP superstructure (IBMS) presented by Isafiade and Fraser (2008) is applied to the design of heat exchanger networks which can handle multiple period of operations. In multi-period operations, parameters such as supply temperature, target temperature and the flowrates of streams can vary over a specified range. In this paper the IBMS is formulated for multi-period operations involving unequal period durations. In order to ensure that each exchanger connecting the same pair of streams in two or more periods is able to transfer heat in such streams for all the periods, the maximum area per period approach of Verheyen and Zhang (2006) is used in the objective function. This method helps to simplify the model. The new method is applied to three examples from the literature. (C) 2010 Published by Elsevier B.V. on behalf of The Institution of Chemical Engineers.