This research concentrates on stochastic optimization models. The research combines Markovian probability analysis, dynamic programming, nonlinear programming, statistical curve fitting, and computer simulation analysis containing sophisticated statistical autoregressive time series methods to investigate the mathematical characteristics of stochastic optimization models. The models relate to decision-making about production and inventory levels, capacity levels, scheduling, and resource allocation. Advanced theoretical analyses are employed to understand the mathematical properties of optimal policies under the most general assumptions that yield analytic solutions. In many cases significant extensions of existing theory are required. The properties of optimal policies are exploited to derive analytic approximations that are numerically accurate and more amenable to computation. Issues of computational simplicity and limited statistical information regarding parameter values are central to motivating the applying statistical estimates as values for the model parameters. In some cases, the approximations can be explicitly modified to accommodate this statistical context, while in other cases the research examines the effects of using standard statistical estimates in place of actual parameter values.
