This study proposes a multi-objective and multi-period mathematical programming model to support planning decisions in the Long-Term Care (LTC) sector. The model provides information to help planning the delivery of institutional LTC services in the medium-term, both in terms of location selection and capacity planning, when it is intended a move towards an equitable provision of care. For this purpose, three equity-related objectives are accounted for—equity of access, geographical equity and socioeconomic equity. Cost considerations are also taken into account. The model objective function incorporates multiple objectives which are scaled into a common unit through weights that are built with the Measuring Attractiveness by a Category-Based Evaluation Technique. The applicability of the model is illustrated through the resolution of a case study in the Great Lisbon region in Portugal.