Strengthening perinatal care provision in medically under-served areas is an important public health task in Korea. Motivated by the ongoing efforts by the Korean government, this paper studies a multi-period capacitated location problem to design an optimal rollout plan for the government's support program. The proposed model incorporates (1) health care consumers' preference for care providers and (2) uncertainty in future demand for perinatal care. If not properly accounted for, these factors render location solutions at risk for under-or over-use, which will result in a continual need for extra budget spending to sustain healthy operation of the care capacities. In the proposed formulation we integrate a discrete choice model that describes the provider choice behavior by women in under-served areas in Korea. In addition, we address the demand uncertainty by using the robust optimization framework. By applying the proposed model to Korea's under-served area support program, we show that both the demand uncertainty and choice behavior significantly influence the solution performance. Furthermore, we find that a strong requirement for robustness drives the model to not open all care provider sites allowed by the program's budget to ensure that the capacity constraints are respected. With this surplus budget, we can relax the robustness requirement to open more perinatal care providers by using the surplus to absorb the cost associated with expected constraint violations. In other words, the surplus budget can pay the price of reducing the price of robustness. (C) 2018 Elsevier B.V. All rights reserved.