In this article, we present a discrete hierarchical location model for public facility planning. The main features of the model are: an accessibility maximization objective; several levels of demand and of facilities; a nested hierarchy of facilities (i.e. a facility of a given level can serve demand of equal and lower levels); maximum and minimum capacity constraints; and user-to-facility assignment constraints. The latter include single-assignment and closest-assignment constraints, as well as a new type of constraints called path-assignment constraints. Their purpose is to enforce some desirable properties for the spatial pattern of assignments. If they are not included, model solutions are difficult to interpret and to explain in a public facility planning context, therefore being less likely to be accepted by the users. The usefulness of the model is illustrated through a real-world application to school network planning.

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(a) to analyse the effect of age on physical fitness (PF) and on-duty task (ODT) performance of male police officers (PO); (b) to analyse the relationship between PF and ODT performance of male PO; and (c) to identify the set of PF attributes which better predicts the ODT performance of male PO. A total of 97 Portuguese male non-elite PO (Public Security Police) took part in this cross-sectional study. Participants were allocated to four age categories (20-29, 30-39, 40-49, and >49 years old), and performed fourteen PF evaluations and one on-duty task simulation test (ODT-ST). MANOVA, partial correlations and multiple linear regression analysis were used. We observed (a) a significant decrease of performance with aging (PF attributes, partial eta-squared=0.763; total time on ODT-ST, partial eta-squared=0.498); (b) significant positive associations between body mass index and fat mass with total time on ODT-ST; (c) a significant negative association between standing broad jump (SBJ), sit-up, push-up, bench-press ratio and aerobic capacity with total time on ODT-ST; and (d) that SBJ, abdominal muscular endurance and aerobic capacity were significant predictors of total time on ODT-ST (R 2 =0.983). PF attributes and ODT performance of Portuguese male non-elite PO decrease significantly with aging. To prevent the observed decrease of performance it seems advisable to implement regular strength and conditioning programmes, which should include muscular power, core strength and aerobic fitness development, to maintain physical capacity and occupational duties.

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In this paper we report the results of a study on secondary school planning made within the framework of Coimbra's Educational Charter. Coimbra is a medium-sized municipality of 320 km2 and 150000 inhabitants located in the center-littoral region of Portugal. The planning problem addressed in the study consisted of defining the location, type, and size of the schools that should integrate Coimbra's secondary school network in 2015, given, first, the excess of aggregate school capacity that currently characterizes the municipality, and, second, the change in school typology that needs to be implemented as a consequence of a recent reorganization of the Portuguese educational system. This problem was analyzed with a discrete facility-location model and considers decisions both of closing existing schools and of opening new schools. The model is a variant of the well-known p-median model, which aims at maximizing the accessibility of students to schools, with constraints on maximum and minimum capacity occupation that make model solutions lose the single assignment and closest assignment properties. As these are desirable properties in a public-facility planning context, they are enforced with explicit constraints. The results obtained through the model are discussed from the standpoint of the trade-off between school accessibility improvements and school network changes.