Inverse and acceptance-rejection strategy are two widely used schemes by various Monte Carlo (MC) methods for handling particle coagulations. They exhibit different algorithm complexity and computational efficiency. In an effort to have a better understanding of the two schemes, we systematically compare their computational performance on CPU and GPUs (graphic processing units) with different computing conditions. The obtained results may serve as a useful guidance on the choice of the particular scheme by various MC methods for handling problems of particle dynamics in practice. (C) 2014 Published by Elsevier B.V.