Modelling Healthcare Facility Location Under Equity and Efficiency Objectives in Borno State Using Bi-Objective Optimization

Healthcare facility location planning in post-conflict environments requires balancing efficiency objectives, such as minimizing total travel distance, against equity objectives that prioritize access for the most vulnerable and geographically isolated populations. This study develops a bi-objective optimization model for healthcare facility location in Borno State, North East Nigeria, incorporating both efficiency and equity criteria within a unified mathematical programming framework. Population demand nodes are constructed from 2023 National Population Commission projections for 412 communities across 27 local government areas, distinguishing between displaced and resident populations. A bi-objective p-median and maximal coverage formulation is solved using the epsilon-constraint method to generate the complete Pareto frontier of non-dominated solutions. Trade-off analysis reveals that improving equity coverage from 70 to 90 percent requires accepting a 23 percent increase in total weighted travel distance, providing policymakers with a quantified representation of the efficiency-equity dilemma. The model is applied under three government budget scenarios corresponding to N500 million, N1 billion, and N2 billion facility construction programmes, generating location recommendations for each budget level. Validation using existing facility performance data confirms model accuracy. The study's bi-objective framework represents a methodological advance over prior single-criterion healthcare location research in Northern Nigeria, and findings directly inform the Borno State Primary Healthcare Development Agency's facility expansion planning. Keywords: bi-objective optimization, healthcare location, equity, Borno State, Pareto frontier