A Two-Stage Optimization Approach for Healthcare Facility Location- Allocation Problems With Service Delivering Based on Genetic Algorithm

This study assesses a multi-period capacitated maximal-covering location-allocation model for healthcare services, taking interservice referral as well as equity access into account. A two-stage optimization strategy is used to formulate the model. In the first stage, facilities are located to maximize covered demand, and in the second stage, patients are allocated to capacitated facilities based on their radius of coverage over multiple time periods. The problem, which belongs to the NP-hard class of optimization problems, is solved using a linear mixed-integer programming (MILP) model. A numerical example is presented to evaluate the efficiency of the proposed model. In addition, to identify near-optimal solutions for large instances, a hybrid genetic-sequential quadratic programming approach (GA-SQP) is developed. To examine the performance and efficiency of the GA-SQP, we employed several randomly generated test instances of various sizes and compared them to those obtained using the exact method. The proposed model has demonstrated an excellent ability in locating healthcare facilities and allocating health services while taking shortage and equity into account during each time period.