Multi-Stage Stochastic Healthcare Resource Allocation under Displacement-Driven Demand Uncertainty: Evidence from Nigeria

Healthcare systems affected by displacement must allocate scarce resources before demand is fully known. This study formulates a three-stage stochastic linear programme for primary healthcare and maternal and newborn health across 177 Nigerian local government areas and 348 supply hubs. Twelve demand states combine four empirical spatial archetypes with severity variation. Controlled comparisons distinguish stochastic initial planning, sequential adaptation and proportional-coverage restrictions. The baseline value of stochastic planning is approximately 0.000338% of expected loss; primary healthcare and maternal and newborn health coverage are 37.74% and 70.96%, respectively. Highly correlated demand vectors, exhausted budgets and shortage-dominated loss accompany the small information gains. Held-out-archetype tests preserve small advantages for stochastic initial plans. Capacity and demand perturbations have larger effects at the levels examined, but capacity expansion at fixed budgets can shift service away from maternal and newborn health. A matched equal-coverage restriction improves minimum local coverage while reducing aggregate service. These conditional planning results distinguish information flexibility from resource scarcity and distributional policy choices.