The development of future More Electric Aircraft (MEA) requires exploitation of lightweighted on-board Electrical Power System (EPS) architectural design and energy saving power management strategies. Seeking for the optimal solutions in these key aspects, two vital prerequisites should be ensured for the entire flight stages with load requirements changesone is the optimal power allocation (OPA) aiming to route the power in the system with less transmission losses, and the other one is the optimal generator sizing (OGS) targeting on minimising the required overload capabilities for a lighter generator. Despite different objectives, these two optimisation problems should both meet the load requirements and system operation constraints, including the power balancing and limitations, contactor switching logic, the transmission losses of cables, and the nonlinear converter efficiencies. In this paper, we first propose a formulation method based on the optimal power flow (OPF) model to constitute the system constraints for both optimisation problem, and combining with specific objectives and constraints, the problems of OPA and OGS can be mathematically modelled. By linearizing the nonlinear transmission efficiencies with piecewise functions, the proposed models can be solved using the mixed-integer linear programming (MILP) in CPLEX solver.