Monte Carlo codes are powerful and accurate tools for reactor core calculations. For coupled core-evolution applications, however, they remain rather demanding on calculation time because of the sheer number of reaction rates required for the evolution calculation. To make Monte Carlo burnup codes more efficient, we must therefore optimize reaction rate calculation to reduce calculation time without loss of accuracy. In the optimal situation, the calculation time of the Monte Carlo burnup code should be as close as possible to that of the basic Monte Carlo simulation. Through a deep analysis of the Monte Carlo simulation process as implemented in MCNP or MCNPX, we have developed an optimum approach called hereafter the multigroup binning approach to reaction rate calculation. In this paper, we have analyzed the performance of the multigroup binning approach as compared to a generic Monte Carlo burnup code. We have implemented this multigroup binning approach into ALEPH, a C++ interface code coupling MCNP or MCNPX, and ORIGEN. A number of validation benchmarks and applications of ALEPH to particular problems such as the rim effect and the High Flux Isotope Reactor of Oak Ridge National Laboratory have also been presented.