We consider a project scheduling problem in a context such that temporal aspects (start and completion of activities, precedence between activities) are handled precisely, while resource consumption is evaluated more roughly over aggregated periods. Hence, the Periodically aggregated Resource-Constrained Project Scheduling Problem (PARCPSP) is well-suited for an intermediate planning/scheduling decision level, in particular with human resources or energetic resources. This problem has been modelled by means of a Mixed Integer Linear Programming (MILP) formulation, based on a mixed time framework. In this extended abstract, we present an alternative way to manage both continuous and discrete temporal representations simultaneously, in order to derive a new MILP formulation for a purpose of theoretical and computational comparison.