This paper provides an overview of various optimization formulations that can lead to improved fuel economy for a series hybrid electric vehicle (HEV). The relevance and improvement to the current state-of-the-art are discussed. The formulated optimal control problems (OCP) consist of two individual optimization challenges: vehicle speed optimization and powertrain power-split optimization. These OCPs can be merged leading to a practical and global problem, where all the aspects are optimized simultaneously for a prescribed route and traveling time. Alternatively, the global problem can be approximated by solving individual OCPs, one for each aspect, in steps and combined a posteriori. The optimal solutions in each case are investigated and compared by simulation examples to expose the trade-off between optimality of fuel economy achieved by global optimization and reduction in computational complexity and hence practicality of the two-step solution approximation.