Many optimization problems that arise in the management sciences involve optimization in the presence of uncertainty. In view of simulation's effectiveness for evaluating complex objective functions that incorporate randomness, it is natural to consider simulation-based optimization algorithms. While much of the existing literature focuses on optimization over a set of continuous decision variables, relatively little has been developed for optimizing, via simulation, an objective function involving discrete decision variables. This is a particularly serious omission since many stochastic optimization problems are most naturally formulated in terms of discrete decision quantities. We propose a gradient--type algorithm that is intended for discrete problems in which the objective varies "smoothly" across the feasible region. Our motivation for considering such a class of problems arose in the setting of a project with a major automaker in which the goal was to optimize the number of containers of different types used to ship parts through its supply chain. The algorithm has the property that in the presence of bounded random variables and "natural convexity", the rate of convergence is of order 1/n. We also present an efficient heuristic algorithm for more general objective functions. The thesis also includes some new results related to simulation-based estimation of a response surface that is either assumed or is known a priori to be convex. We discuss how the convexity can be exploited to obtain a better estimate of the response surface than would be possible in the absence of convexity. The thesis concludes with some recent work on a class of modeling questions that arise when initializing simulations that are used as part of a decision tool to predict system performance over a finite horizon.
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