Theoretical Advances in Robust Optimization for Humanitarian Logistics Network Design in Conflict-Affected Environments

Humanitarian logistics network design in conflict-affected environments confronts extreme uncertainty regarding demand locations, road network accessibility, facility security, and supply availability, exceeding the representational capacity of conventional stochastic programming models that assume well-characterized probability distributions. This dissertation advances robust optimization theory and methodology for humanitarian logistics network design in conflict-affected environments, drawing on empirical grounding from Nigeria's North East geopolitical zone. A critical review of humanitarian operations research literature identifies the prevailing reliance on scenario-based stochastic models and articulates a theoretical case for distribution-free robust formulations better suited to genuine deep uncertainty. The dissertation makes three original theoretical contributions: an extended moment-based robust optimization framework that incorporates structural information about demand and network uncertainty without distributional assumptions; a novel decomposition algorithm for large-scale robust facility location problems under uncertainty set structures relevant to conflict environments; and a bi-level robust model capturing adversarial route interdiction alongside uncertain demand. Theoretical results include optimality conditions, duality relationships, and worst-case approximation guarantees for each model class. Empirical validation uses an original dataset of humanitarian operations in Borno, Yobe, and Adamawa States compiled through collaboration with humanitarian organizations. Results demonstrate that robust designs achieve 41 percent lower worst-case unmet demand than stochastic designs calibrated on historical scenarios when novel disruption patterns materialize. This dissertation contributes to robust optimization theory, humanitarian operations research, and conflict zone logistics practice. Keywords: robust optimization, humanitarian logistics, conflict environment, facility location, North East Nigeria