This paper addresses the problem of modeling and estimating the cost of the heat exchanger network (HEN) in multi-period operation using pinch technique concepts. The developed method improves the vertical heat exchanges technique originally proposed by Ahmad et al., by estimating the contribution of each stream to the overall HEN area instead of equally distributing the area between the computed minimum number of exchangers. This method allows to consider the available area for each stream and to manage the fact that some streams may not be active during some particular periods of operation. The method proposed computes the near-optimal DTmin/2 contribution, associated to the streams in each of the periods, from one single reference value. This allows to reduce the number of decision variables to one, when computing the energy saving/investment trade-off in thermo-economic optimisation models.