Modeling a robust 2-service community healthcare network design problem with central hospital congestion

We address a more realistic variant of the community healthcare network design problem, considering a 2-service network framework and hospital congestion structures. Our objective is to minimise the total expected cost through strategic location of central hospitals and allocation of community health stations. Notably, each community health station is allocated to exactly two central hospitals. We also account for uncertainties in resident medical demands, which are challenging to predict accurately due to their volatility. To tackle this, we propose an adaptive distributionally robust optimisation approach that confines uncertain variables to an ambiguity set reflecting demand distribution characteristics. To enhance tractability, we reformulate the distributionally robust model as a mixed-integer linear programme within the specified ambiguity set. Numerical experiments on a real case demonstrate the validity and superiority of the proposed model. Finally, the impact of uncertainty is discussed in depth and some managerial insights for healthcare managers are summarised.