Optimal Allocation of Emergency Relief Supplies Using Linear Programming in Adamawa State

The efficient allocation of emergency relief supplies during humanitarian crises is a critical challenge in Nigeria's North East geopolitical zone, where recurrent insurgency-related displacements have strained government and non-governmental response capacities. This study applies linear programming to model the optimal allocation of food, medical kits, and shelter materials across 12 internally displaced persons (IDP) camps in Adamawa State during a simulated emergency scenario. Data on camp population sizes, supply quantities available at three distribution hubs, transportation costs, and minimum daily ration requirements per person were obtained from the National Emergency Management Agency and two active non-governmental organizations operating in the state. A minimization LP model is formulated to minimize total transportation and distribution cost subject to supply availability, camp demand satisfaction, and vehicle capacity constraints. The simplex method is applied to derive the optimal distribution plan. Results demonstrate that the current ad hoc distribution approach incurs approximately 31 percent higher costs than the LP-optimal plan and leaves two camps chronically undersupplied. The LP solution ensures all camp minimum requirements are met at minimum total cost. Recommendations include establishing a digital supply allocation system within the state emergency operations centre and training logistics officers in basic LP model use. This study contributes a scalable quantitative methodology for humanitarian logistics planning in conflict-affected regions of Nigeria. Keywords: linear programming, emergency relief, IDP camps, Adamawa State, humanitarian logistics