A dynamic programming-based algorithm is used for off-line optimisation of control variables of a series-parallel extended range electric vehicle powertrain. The aim is to minimise the fuel and/or electricity consumption, subject to battery state-of-charge constraints and physical limits of different powertrain variables. The optimised control variables include engine torque and electric machine speed, as well as a variable that selects the powertrain operating mode defining the state of powertrain clutches. The optimisation results are presented for four characteristic certification driving cycles and different vehicle operating regimes including electric driving during charge depleting (CD) regime, hybrid driving during charge sustaining (CS) regime, and combined/blended regime. The emphasis is on the blended regime and a related analysis of fuel saving potential when compared to the CD-CS regime. The optimisation results are used to provide recommendations for design of a realistic (on-line) control strategy that is a subject of another publication.