SummaryIn this paper we provide a computation algorithm to get a global solution for the maximum rank correlation estimator using the mixed integer programming (MIP) approach. We construct a new constrained optimization problem by transforming all indicator functions into binary parameters to be estimated and show that it is equivalent to the original problem. We also consider an application of the best subset rank prediction and show that the original optimization problem can be reformulated as MIP. We derive the nonasymptotic bound for the tail probability of the predictive performance measure. We investigate the performance of the MIP algorithm by an empirical example and Monte Carlo simulations.