Robust multi-period capacity, location, and access of rural cardiovascular services under uncertainty

Ensuring timely access to specialty healthcare in rural areas is challenging due to long appointment delays, travel distances, budget limitations, and capacity restrictions. Since capacity and resource allocation decisions are often made infrequently, unanticipated population changes, for example, can render current good solutions ineffective for future challenges. To meet long-term care needs under uncertainty, single-period and multi-period optimization models are developed to optimize practice locations, clinician staffing, and assignment of patients which accounts for uncertainty and variation in acuity, demand volume, and long-term provider capacity. The objective is to improve access and care continuity by minimizing patient travel and appointment delays, out-of-network referrals, and practice costs. Deterministic, robust, and chance-constrained optimization models are developed, and their results are compared and applied to a large health system for cardiovascular services in Maine, United States. Through scenario analysis, we show which resources are the most critical and what helps increase patients’ access. More generally, considering multiple-periods and uncertainty at the same time when allocating resources help health systems make important capacity planning decisions in the presence of uncertain future demand. For both single- and multiple-periods, the robust model requires more staff in general to keep a comparable number of zip codes covered with a minimal increase in operating costs. The solution under the chance-constrained model is very similar to the deterministic one; this shows that the deterministic solution is feasible in 95% of most the cases.