Multi-Level Robust Optimization: Theory, Algorithms and Practice

In practice, decision-problems which concern planning horizons spanning several months or years will typically involve various sources of uncertainty, and in many cases these uncertainties will impact decisions over differing time-scales and in different levels of the problem. Accurately accounting for these uncertainties in an optimization model is challenging with traditional approaches, as all uncertainties would generally be treated simultaneously. The proposed project aimed to develop novel optimization theory and methodologies to tackle multi-level robust optimization problems with efficient algorithmic approaches. A range of practical problems from the domains of manufacturing and health systems were identified as ideal candidates to enable the broader research goals: production planning under uncertainty (where uncertain parameters were novel, e.g., timing of a delivery rather than quantity), complex manufacturing problems that integrate often competing decisions in different levels (e.g., lot-sizing and cutting stock), and healthcare staff scheduling that contain many real-world constraints. The project successfully concluded with an extensive range of theoretical results including mathematical properties of specific problem structures or competing uncertainties, equivalence/strength of alternative formulations, and problem complexities. Moreover, a rich range of algorithms were proposed and evaluated, including dynamic programming algorithms that work in polynomial time in certain cases, sophisticated multi-stage algorithms to handle uncertainties in a systematic fashion, and heuristic algorithms for computationally challenging real-world settings. Three peer reviewed journal articles were developed and submitted from this research. At this time one of the submissions has been accepted.