EFFICIENT MULTINOMIAL SELECTION IN SIMULATION

Consider a simulation experiment consisting of upsilon independent vec tor replications across k systems, where in any given replication one system is selected as the best performer (i.e., it wins). Each system has an unknown constant probability of winning in any replication and the numbers of wins for the individual systems follow a multinomial di stribution. The classical multinomial selection procedure of Bechhofer , Elmaghraby, and Morse (Procedure BEM) prescribes a minimum number of replications, denoted as upsilon, so that the probability of correct ly selecting the true best system (PCS) meets or exceeds a prespecifie d probability. Assuming that larger is better, Procedure BEM selects a s best the system having the largest value of the performance measure in more replications than any other system. We use these same upsilon replications across k systems to form (upsilon)(k) pseudoreplication s that contain one observation from each system, and develop Procedure AVC ((A) under bar ll (V) under bar ector (C) under bar omparisons) t o achieve a higher PCS than with Procedure BEM. For specific small-sam ple cases and via a large-sample approximation we show that the PCS wi th Procedure AVC exceeds the PCS with Procedure BEM. We also show that with Procedure AVC we achieve a given PCS with a smaller upsilon than the upsilon required with Procedure BEM. (C) 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 459-482, 1998.