Motivated by the practical needs in simulation optimization, this paper considers the problem of selecting the best m and worst n designs from a total of k alternatives based on their mean performance values, which are unknown and can only be estimated via simulation. In order to improve the efficiency of simulation, this research characterizes an asymptotically optimal allocation of simulation replications among the k designs such that the probability of correctly selecting the best m and worst n designs can be maximized, and develops a corresponding selection procedure for implementation purpose. The efficiency of the proposed procedure is demonstrated via numerical experiments. (C) 2017 Elsevier Ltd. All rights reserved.