LP-GP Optimization Model for Allocation of Relief Materials to Internally Displaced Persons Camps in Abuja, Nigeria

This paper presents an optimization model for the equitable and cost-effective allocation of relief materials to internally displaced persons (IDP) camps in Abuja, Nigeria. Due to the inherent challenges of humanitarian logistics, including data uncertainty and complex supply chains, this study employs a robust linear programming–geometric programming (LP–GP) hybrid model to determine the optimal monthly distribution cost from available semi-annual budgets. The LP–GP hybrid model offers a significant advantage over traditional linear programming by providing a globally optimal solution even when initial budget data may be inflated or unreliable, thereby addressing a critical challenge in humanitarian contexts such as financial leakages. Using data from five IDP camps for the first half of 2024, sourced from the National Emergency Management Agency (NEMA) and inter-agency registration exercises, the study identifies an optimal monthly distribution cost of ₦62,932,233 (approximately ₦377.6 million semi-annually), representing a 95.3% reduction relative to the allocated budget of ₦8.01 billion. The robustness of the model is examined under varying input parameters, confirming the independence of the optimal cost from the potentially inflated allocated budget. The findings highlight substantial potential for improved efficiency and resource management through the adoption of a data- driven, harmonized distribution system. The paper recommends that government agencies such as NEMA adopt this optimization approach to enhance transparency and sustainability in humanitarian aid distribution.