Assessing performance in health care: A mathematical programming approach for the re-design of primary health care networks

Mathematical models allow studying complex systems. In particular, optimal facility location models provide a sound framework to assess the performance of first-level of health care networks. In this work, a methodology founded on need/offer/demand quantification through a facility location-based mathematical model is proposed to assess the performance of existing networks of Primary Health Care Centers (PHCC) and assist in its re-design. The proposed re-design problem investigates the re-allocation of existing resources within the given infrastructure (existing PHCCs) to better satisfy the estimated health needs of the target population. This problem has not been widely addressed in the open literature despite its paramount importance in modern societies with fast demographic dynamics and constrained investment capacities. The model seeks to optimally assign the required type of service and the corresponding capacity to each PHCC (offer). The objective function to be maximized is the number of (needed) patients’ visits effectively covered by the network (demand). The following constraints are explicitly considered: i) geographic accessibility from need centers to PHCCs, ii) maximum delivery capacity of each service in each PHCC, and iii) total budget regarding fixed, variable, and relocation costs. The proposed methodology was applied to a medium-size city. Results show that the non-attended necessity can be reduced by introducing capacity modifications in the existing network. Moreover, different solutions are obtained if budgetary restrictions or minimum attention volume constraints are included. This reveals how model-based decision support tools can help health decision-makers assessing primary health care network performance.