Distributionally Robust Scheduling of Food Water Energy Nexus Environmental Systems in Uganda: Reliability Guarantees Under Demand and Failure Uncertainty

Operational scheduling of integrated food, water and energy systems in Uganda confronts a dual uncertainty: stochastic variability in demands and the discrete risk of infrastructure failure. Conventional stochastic programming requires exact distributional knowledge that operators rarely possess, while robust optimisation anchored to unbounded ambiguity sets yields excessively conservative schedules. The framework minimises expected operational cost subject to conditional value-at-risk constraints on supply shortfalls, thereby providing explicit reliability guarantees that hold uniformly over the ambiguity set. A structural result establishes that the resulting optimisation problem admits a tractable semidefinite programming reformulation, and a decomposition algorithm is proposed for large-scale nexus networks. The analysis further demonstrates how the framework accommodates Ugandan institutional realities, including irrigation-electricity trade-offs in the Nile basin and biomass dependence in rural energy systems, without requiring proprietary data. The principal contribution is a methodological bridge between moment-based distributional robustness and reliability-constrained scheduling that yields verifiable service-level guarantees under precisely the uncertainty conditions characteristic of infrastructure systems in low-income countries.