The P-graph (process graph) framework is an effective tool for process-network synthesis (PNS). Here we extended it to multi-period operations. The efficacy of the P-graph methodology has been demonstrated by numerous applications. The unambiguous representation of processes and the availability of the axioms defining combinatorially feasible structures facilitates the development of efficient algorithms to determine maximal structures, solution structures, and optimal structure for processes. However, it is presumed that single-period operation prevails. It implies that the operating conditions and the load of each operating unit remain unchanged, i.e., steady-state operation. This is usually true for the chemical industry but often not in agriculture or where seasonal effects are important. The current work proposes a multi-period operation wherein the load of operating units varies from period to period to accommodate demand, assuming operating conditions remain steady in each period. A modeling technique is proposed to represent operating units in the multi-period operation. The different periods are connected by "fictitious" streams, which ensures, that the unit is sized properly. (C) 2015 Elsevier Ltd. All rights reserved.