This work proposes a sequential approach for the multi-period synthesis of Heat Exchanger Networks (HEN) and Utility Systems of chemical processes and energy systems, including thermal, electric and material storage. The optimization approach is sequential and it consists in three steps: (1) the multi-period Mixed Integer Linear Programming (MILP) energy integration model of Marechal and Kalitventzeff (2003) determines the optimal utility selection, size and operation scheduling (on/off) as well as the size of the storage system which minimize the linearized utility total costs for given Heat Recovery Approach Temperature (HRAT), (2) a modified version of the multi-period MILP minimum number of units problem Floudas and Grossmann (1986) determines the number of matches (heat exchanger units) between hot and cold streams such that the sum of the associated penalty levels are minimized, (3) the Non Linear Programming (NLP) multi-period HEN synthesis model proposed by Floudas and Grossmann (1987) finds the HEN with minimum area. In order to partially overcome limitations of the sequential approach, HRATs for each stream and for each time period, as well as penalty levels associated to each possible exchange and the sizes of available utilities are optimized using the derivative-free hybrid algorithm PGS-COM Martelli and Amaldi (2014).