Optimal Location Planning for Health Centres in Rural Communities of Zamfara State Using Set Covering Models

Access to primary healthcare remains severely limited in rural Zamfara State, North West Nigeria, where geographic dispersion, poor road networks, and inadequate facility distribution leave large populations outside acceptable travel distance of the nearest health centre. This study applies the set covering location model to determine the minimum number and optimal placement of primary health centres required to ensure that every community within Zamfara's rural zones is served within a 10-kilometre travel distance. Geographic and population data for 318 rural communities are compiled from National Population Commission estimates and satellite imagery. A binary set covering model is formulated with communities as demand nodes and candidate facility sites as decision variables. A greedy heuristic is applied to solve the large-scale binary programme, and results are validated against an exact integer programming solution for a reduced problem subset. Findings indicate that 24 optimally sited health centres can achieve full population coverage within the 10-kilometre threshold, compared to the 31 currently operating facilities that leave 19 percent of communities uncovered. The model identifies 11 candidate sites where new facilities would most efficiently expand coverage. Recommendations include using the model output to guide the State Primary Healthcare Development Agency's facility placement decisions and revising the siting criteria for new construction projects. This research provides a direct planning contribution to improving healthcare access equity in one of Nigeria's most underserved states. Keywords: set covering model, health centre location, Zamfara State, rural healthcare access, facility planning