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Efficient multinomial selection in simulation. (English) Zbl 0940.90062
Summary: Consider a simulation experiment consisting of $$v$$ independent vector 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 distribution. The classical multinomial selection procedure of Bechhofer, Elmaghraby, and Morse (BEM) prescribes a minimum number of replications, denoted as $$v^*$$, so that the probability of correctly selecting the true best system (PCS) meets or exceeds a prespecified probability. Assuming that larger is better, BEM selects as best the system having the largest value of the performance measure in more replications than any other system. We use these same $$v^*$$ replications across $$k$$ systems to form $$(v^*)^k$$ pseudoreplications that contain one observation from each system, and develop AVC (All Vector Comparisons) to achieve a higher PCS than with BEM. For specific small-sample cases and via a large sample approximation we show that the PCS with Procedure AVC exceeds the PCS with BEM. We also show that with AVC we achieve a given PCS with a smaller $$v$$ than the $$v^*$$ required with BEM.

##### MSC:
 90B99 Operations research and management science
##### Keywords:
multinomial; ranking and selection; simulation
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