The MBD@rsSCS model coupled to DFT methods involves a small additional computational cost compared to the solution of the KS equations, however, for increasingly large systems where linear-scaling DFT methods are employed, the O(N 3 ) scaling of the diagonalization procedure as well as the solution of the self-consistent screening equations becomes no longer negligible. In the present work, we considerably extend the applicability of the MBD@rsSCS model via a novel computational resolution of its equations. A robust and efficient linear-scaling scheme for the iterative solution of the self-consistent screening equations is introduced together with a stochastic approach allowing for a linear scaling estimation of the MBD energy which bypasses matrix diagonalization. The article is organized as follows: first the MBD@rsSCS model is briefly reviewed at the beginning of the Theory section. Later in the same section the theoretical aspects of the efficient solution of rsSCS equations are presented as well as the theoretical foundations of the linear-scaling stochastic estimator of the MBD energy. A detailed discussion of the algorithms and of their massively parallel implementations are presented in the Numerical Result section that is followed by the Conclusion.