6. A Comparative Study of Procedures for the Multinomial Selection Problem

This paper is concerned with the multinomial selection problem (MSP) originally formulated by Bechhofer, Elmaghraby, and Morse (1959). Over the past 50 years, numerous procedures have been developed for finding the most probable multinomial alternative; these procedures attempt to minimize the expected number of trials while exceeding a lower bound on the probability of making a correct selection when the multinomial probabilities satisfy an indifference-zone probability requirement. We examine such MSP procedures, including optimal procedures based on new linear and integer programming methods, provide more accurate and extensive parameter and performance tables for several procedures, and calculate and compare the exact efficiencies of the procedures.