A robust optimization model for tactical capacity planning in an outpatient setting

Tactical capacity planning is a key element of planning and control decisions in healthcare settings, focusing on the medium-term allocation of a clinic's resources to appointments of different types. One of the most scarce resources in healthcare is physician time. Due to uncertainty in demand for appointments, it is difficult to provide an exact match between the planned physician availability and appointment requests. Our study uses cardinality-constrained robust optimization to develop tactical capacity plans which are robust against uncertainty, providing a feasible allocation of capacity for all realizations of demand to the extent allowed by the budget of uncertainty. The outpatient setting we consider sees first-visit patients and re-visit patients, and both patient types have access time targets. We experimentally evaluate our robust model and its practical implications under different levels of conservatism. We show that we can guarantee 100% feasibility of the robust tactical capacity plan while not being fully conservative, which will lead to the clinic saving money while being able to meet demand despite uncertainty. We also show how the robust model helps us to identify the critical time periods leading to worst case physician peak load, which could be valuable to decision-makers. Throughout the experiments, we find that the step of translating available data into an uncertainty set can influence the true conservatism of a solution.