Balancing shortage risk and equity in healthcare allocation under displacement-driven demand uncertainty in Nigeria A multistage stochastic optimisation study

Abstract Background Displacement can alter healthcare requirements before resources can be procured and deployed. Health planners must balance aggregate service, severe shortages and geographic priorities. We examined whether protecting adverse system losses and extreme-demand conditions also protects primary healthcare and maternal and newborn health provision. Methods We formulated a three-stage stochastic linear programme for 177 local government areas and 348 supply hubs in ten Nigerian states. Four displacement-derived archetypes and three severity levels generated twelve planning scenarios. Matched comparisons evaluated expected-loss minimisation, conditional value-at-risk, geographic priority penalties and a shortage cap in a preselected extreme-demand scenario. We assessed resource-specific coverage, geographic outcomes, shortage feasibility and sensitivity to resource conditions and priority construction. A separate extension imposed minimum maternal and newborn health coverage in every scenario. Results At the assumed probabilities, 95% conditional value-at-risk equalled maximum scenario loss. Risk aversion produced small loss reductions. Compared with expected-loss minimisation, the integrated policy reduced the penalty-weighted priority increment by 4.087% and pooled priority-weighted shortage by 0.168%, while expected base loss increased by 0.033%. Primary healthcare coverage remained 37.743%, but maternal and newborn health coverage declined from 70.959% to 70.309%; geographic effects were mixed. Minimum protected shortage was only 20.266 pooled units below the reference cap. Secondary expected-loss minimisation approached this minimum while preserving most non-protected service. The largest feasible common maternal and newborn health coverage floors were 62.716% at baseline capacity and 64.907% at 120% capacity with unchanged budgets. At expanded capacity, feasible positive floors prevented zero maternal and newborn health allocation, at higher expected loss and lower primary healthcare coverage. Conclusions Loss protection and geographic priorities do not guarantee resource-specific service adequacy. Planners should specify protected services, test target feasibility and examine geographic and resource-specific trade-offs together. These findings concern a calibrated planning system; they do not demonstrate observed utilisation gains or clinical benefit.