Distributionally Robust Scheduling of Food Process Engineering Systems in Uganda: Reliability Guarantees Under Demand and Failure Uncertainty

Scheduling food process engineering systems in Uganda must contend with two compounding uncertainties: volatile demand for processed products and stochastic equipment failures that disrupt production lines. Conventional stochastic programming requires exact probability distributions for these uncertainties, yet Ugandan food processors rarely possess sufficient historical data to specify such distributions reliably. The framework formulates the scheduling problem as a two-stage optimisation in which first-stage decisions fix production quantities and maintenance windows, while second-stage recourse actions respond to realised demand shortfalls and equipment outages. Using duality theory, the distributionally robust problem is reformulated as a tractable semidefinite programme whose optimal value provides a worst-case expected cost guarantee over all distributions consistent with the specified moments. The analysis establishes that the ambiguity set's size parameterises a continuum between deterministic scheduling and fully robust interval-based scheduling, enabling engineers to calibrate conservatism against available data. A case structure based on a typical Ugandan maize milling facility illustrates how the framework generates schedules with explicit reliability certificates, expressed as upper bounds on expected shortfall probability. The principal contribution is a computationally implementable method that converts partial distributional knowledge into verifiable reliability guarantees, addressing a core constraint of food process engineering in data-scarce environments.