A multi-period multi-criteria districting problem applied to primary care scheme with gradual assignment

We present a modeling and optimization approach for the planning of primary healthcare services in order to efficiently direct patient admissions to general practitioners (GP) and to leverage the capacity of the healthcare system. We propose a multi-period multi-criteria districting model for the problem of designing GP districts in the presence of six criteria: workload balance, capacity, accessibility, compactness, income equity, and district similarity. We combine the last three criteria into a single objective function and formulate the problem as a mixed integer program with binary location decision variables and relaxed allocation decision variables for gradual assignments. To assess the usefulness of the model, we test it on real-case scenarios in Istanbul, Turkey.