| The trustworthiness of models and optimization is limited because the associated systems might be changing and data about them can be limited, i.e., there is "parametric" uncertainty. This dissertation provides applications and theory related to mitigating the effects of changing systems and data limitations in optimal decision-making.;The primary application considered relates to reducing the maintenance costs associated with cyber security. By selecting optimal policies addressing data limitations, losses from stolen information and maintenance costs can be balanced. The approximated expected savings from implementing the suggested policies at a large Midwestern organization is over ;The dissertation also integrates data and dynamic programming models for project management decision-making that accounts for coordination and planning costs. This facilitates more accurate schedules with significant cost savings. Insights are provided into the choice between traditional planning methods and agile project management methods that reduce planning complexity. In many situations, we find that the so-called optimal approaches are suboptimal because they fail to address sizable coordination and planning costs.;Two types of parametric uncertainty are explored here, each of which results in fundamentally different formulations and solution schemes. The first type of uncertainty considered relates to system parameters fluctuating over time randomly. The related models differ from ordinary inhomogeneous approaches because the specific parameters are not known and are assumed to fluctuate with known distributions. Associated decision problems are referred to as "Markov decision processes with random inhomogeneity" and proposed optimal solutions methods. Proof is given that the solution produced by backward induction is optimal for the finite horizon problems, and that the value-iteration-based algorithm gives solutions converging to the infinite horizon solutions, together with results regarding monotonicity property and rate of the convergence.;The second type of parametric uncertainty is caused by insufficient data for parameter estimation, i.e., "data-driven" uncertainty. Previous researchers studying data-driven Markov decision processes declare the problem is intractable. Therefore, they propose approximation methods. We prove that their methods can approximate suboptimal solutions by a numerical example. We also provide a dynamic programming algorithm to generate data-driven optimal policies with learning. We do this by demonstrating that the problem is equivalent to partially observable Markov decision processes. Further, by exploiting the structure of the problem and bounds assuming perfect information, we develop a bounding heuristic method for the infinite horizon problems. |
