Simulation Optimization: New Methods and An Application
Fu, Michael C
Ryzhov, Ilya O
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Simulation models are commonly used to provide analysis and prediction of the behavior of complex stochastic systems. Simulation optimization integrates optimization techniques into simulation analysis to capture response surface, to choose optimal decision variables and to perform sensitivity analysis. Objective functions usually cannot be computed in closed form and are computationally expensive to evaluate. Many methods are proposed by researchers for problems with continuous and discrete variables, respectively. The dissertation is comprised of both optimization methods and a real-world application. In particular, our goal is to develop new methods based on direct gradient estimates and variational Bayesian techniques. The first part of the thesis considers the setting where additional direct gradient information is available and introduces different approaches for enhancing regression models and stochastic kriging with this additional gradient information,respectively. For regression models, we propose Direct Gradient Augmented Regression (DiGAR) models to incorporate direct gradient estimators. We characterize the variance of the estimated parameters in DiGAR and compare them analytically with the standard regression model for some special settings. For stochastic kriging, we propose Gradient Extrapolated Stochastic Kriging (GESK) to incorporate direct gradient estimates by extrapolating additional responses. We show that GESK reduces mean squared error (MSE) compared to stochastic kriging under certain conditions on step sizes. We also propose maximizing penalized likelihood and minimizing integrated mean squared error to determine the step sizes. The second part of the thesis focuses on the problem of learning unknown correlation structures in ranking and selection (R&S) problems. We proposes a computationally tractable Bayesian statistical model for learning unknown correlation structures in fully sequential simulation selection. We derive a Bayesian procedure that allocates simulations based on the value of information, thus anticipating future changes to our beliefs about the correlations. The proposed approach is able to simultaneously learn unknown mean performance values and unknown correlations, whereas existing approaches in the literature assume independence or known correlations to learn unknown mean performance values only. Finally we consider an application in business-to-business (B2B) pricing. We propose an approximate Bayesian statistical model for predicting the win/loss probability for a given price and an approach for recommending target prices based on the approximate Bayesian model.