Multinomial selection problem procedures are ranking and selection techniques that aim to select the best (most probable) alternative based upon a sequence of multinomial observations. The classical formulation of the procedure design problem is to find a decision rule for terminating sampling. The decision rule should minimize the expected number of observations taken while achieving a specified indifference zone requirement on the prior probability of making a correct selection when the alternative configurations are in a particular subset of the probability space called the preference zone. We study the constrained version of the design problem in which there is a given maximum number of allowed observations. Numerous procedures have been proposed over the past 50 years, all of them suboptimal. In this thesis, we find via linear programming the optimal selection procedure for any given probability configuration. The optimal procedure turns out to be necessarily randomized in many cases. We also find via mixed integer programming the optimal non-randomized procedure. We demonstrate the performance of the methodology on a number of examples. We then reformulate the mathematical programs to make them more efficient to implement, thereby significantly expanding the range of computationally feasible problems. We prove that there exists an optimal policy which has at most one randomized decision point and we develop a procedure for finding such a policy. We also extend our formulation to replicate existing procedures. Next, we show that there is very little difference between the relative performances of the optimal randomized and non-randomized procedures. Additionally, we compare existing procedures using the optimal procedure as a benchmark, and produce updated tables for a number of those procedures. Then, we develop a methodology that guarantees the optimal randomized and non-randomized procedures for a broad class of variable observation cost functions -- the first of its kind. We examine procedure performance under a variety of cost functions, demonstrating that incorrect assumptions regarding marginal observation costs may lead to increased total costs. Finally, we investigate and challenge key assumptions concerning the indifference zone parameter and the conditional probability of correct selection, revealing some interesting implications.

ANOVA analysis is a classic tool for multiple comparisons and has been widely used in numerous disciplines due to its simplicity and convenience. The ANOVA procedure is designed to test if a number of different populations are all different. This is followed by usual multiple comparison tests to rank the populations. However, the probability of selecting the best population via ANOVA procedure does not guarantee the probability to be larger than some desired prespecified level. This lack of desirability of the ANOVA procedure was overcome by researchers in early 1950's by designing experiments with the goal of selecting the best population. In this dissertation, a single-stage procedure is introduced to partition k treatments into "good" and "bad" groups with respect to a control population assuming some key parameters are known. Next, the proposed partition procedure is genaralized for the case when the parameters are unknown and a purely-sequential procedure and a two-stage procedure are derived. Theoretical asymptotic properties, such as first order and second order properties, of the proposed procedures are derived to document the efficiency of the proposed procedures. These theoretical properties are studied via Monte Carlo simulations to document the performance of the procedures for small and moderate sample sizes.

Several exact and approximate dynamic programming formulations have already been proposed to solve hotel revenue management (RM) problems. To obtain tractable solutions, these methods are often bound by simplifying assumptions which prevent their application on large and dynamic complex systems. This dissertation introduces HotelSimu, a flexible simulation-based optimization approach for hotel RM, and investigates possible approaches to increase the efficiency of black-box optimization methods in the presence of noise. In fact, HotelSimu employs black-box optimization and stochastic simulation to find the dynamic pricing policy which is expected to maximize the revenue of a given hotel in a certain period of time. However, the simulation output is noisy and different solutions should be compared in a statistically significant manner. Various black-box heuristics based on variations of random local search are investigated and integrated with statistical analysis techniques in order to manage efficiently the optimization budget.

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