Distributionally Robust Scheduling of Food Systems Interdisciplinary Incl Agri Systems in Uganda: Reliability Guarantees Under Demand and Failure Uncertainty

The analysis demonstrates that when the true probability distributions of demand shocks and component failure times are imperfectly known, nominal schedules derived from assumed distributions can violate service reliability constraints with unacceptable frequency. We construct an ambiguity set based on moment information and formulate a two-stage distributionally robust scheduling problem that minimises expected operational cost while guaranteeing that reliability constraints hold for all distributions within the ambiguity set. The principal contribution is a proof that the resulting semi-infinite program admits an equivalent tractable reformulation as a second-order cone program when the ambiguity set is defined by first and second moment bounds. A case-oriented discussion situates the framework within Ugandan food systems, where post-harvest losses, intermittent energy supply and fragmented cold-chain infrastructure amplify the consequences of scheduling decisions made under deep uncertainty. The paper concludes that distributionally robust scheduling offers a principled alternative to scenario-based approaches, providing explicit reliability guarantees without requiring precise distributional knowledge that is rarely available in practice.