A Comparative Study of Procedures for the Multinomial Selection Problem
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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.
KeywordsMultinomial selection problem Indifference zone Ranking and selection.
- Bartholdi, J. J. (2010). The Great Package Race, The Supply Chain & Logistics Institute. Atlanta: Georgia Institute of Technology. www2.isye.gatech.edu/people/faculty/John_Barth-oldi/wh/package-race/package-race.html. Accessed 20 June 2012.Google Scholar
- Bechhofer, R. E., & Goldsman, D. (1986). Truncation of the Bechhofer-Kiefer-Sobel sequential procedure for selecting the multinomial event which has the largest probability (II): Extended tables and an improved procedure. Communications in Statistics—Simulation and Computation B15, 829–851.CrossRefGoogle Scholar
- Bechhofer, R. E., Kiefer, J., & Sobel, M. (1968). Sequential Identification and Ranking Procedures (with Special Reference to Koopman-Darmois Populations). University of Chicago Press: Chicago.Google Scholar
- Bechhofer, R. E., & Kulkarni, R. V. (1984). Closed sequential procedures for selecting the multinomial events which have the largest probabilities. Communications in Statistics—Theory and Methods A13, 2997–3031.Google Scholar
- Bechhofer, R. E., Santner, T. J., & Goldsman, D. (1995). Design and Analysis of Experiments for Statistical Selection, Screening and Multiple Comparisons. John Wiley and Sons: New York.Google Scholar
- Cacoullos, T., & Sobel, M. (1966). An inverse sampling procedure for selecting the most probable event in a multinomial distribution. In P. Krishnaiah (Ed.), Multivariate Analysis (pp. 423–455) New York: Academic Press.Google Scholar
- Tollefson, E. (2012). Optimal Randomized and Non-Randomized Procedures for Multinomial Selection Problems, Ph.D. dissertation, H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA.Google Scholar
- Tollefson, E., Goldsman, D., Kleywegt, A., & Tovey, C. (2013). Optimal selection of the most probable multinomial alternative. In review.Google Scholar