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This article deals with social infrastructure planning problems of the following type. Authorities want to determine where to locate the facilities of a social infrastructure network and what should be the capacity of these facilities. Each user must be assigned to its closest facility and, to be economically viable, each facility must serve at least a pre-specified level of demand. The objective is to maximize the accessibility to facilities (i.e., to minimize the distance traveled by users to reach the facilities). A location model that captures the above features is formulated and different solution methods are tested. Among the methods tested, tabu search and a specialized local search heuristic provided the best solutions. The application of the model is illustrated through a case study involving the location of preschools in the municipality of Miranda do Corvo, Portugal.

IntroductionThe quality of life in cities and regions depends strongly on the accessibility of their population to services such as education, health care, public safety, and justice. For this reason the decisions regarding the location and size of the facilities associated with those services need to be carefully planned.Very often decisions of that kind are made in the context of spatial development plans through a comprehensive approach. When this is the case, rather than defining whether a particular facility should be located in a particular urban center in some region, planners will typically aim at defining the region's urban hierarchy öthat is, the level of hierarchy to assign to the urban centers of the region, each level being characterized by a class of facilities. For instance, in a three-level hierarchy, facilities such as elementary schools or basic health care units could be associated with firstlevel centers, whereas secondary schools and local hospitals could be associated with second-level centers, and universities and central hospitals with third-level centers. Note that centers at the higher levels of hierarchy are typically assumed to have all lower level facilities as well (or, in the case of facilities such as hospitals, to be able to provide all services available at lower level facilities).The decision to elevate an urban center to a new level of hierarchy implies a large investment of public funds, opening of new job opportunities, relocation of associated`spin-off' industries, etc ö all of these factors likely leading to significant increases of population at the`elevated' centers, with corresponding future increases of demand for services. Of course, these increases in population are likely to be due

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Spatial planners often make “comprehensive” decisions on the location of public service facilities by using the concept of urban hierarchy: population centers at the upper level of the hierarchy (typically large cities) get the highest level facilities, such as specialized hospitals and universities, while the centers at the lower levels of hierarchy get lower-level facilities. Intuitively, this suggests that there should be a link between urban hierarchy designations and population dynamics in future periods. This link must be taken into account in planning decisions, as it suggests that today’s decisions affect tomorrow’s demand for services. Indeed, this link was assumed in a previously published planning model. Yet, no direct evidence of such a link appears in the literature. The primary goal of this article is to fill this gap by using the census data for Portugal for the period 1991–2001 and the changes in the urban hierarchy that were implemented during 1980s and early 1990s. While our results support the link between urban hierarchy designations and population dynamics that has been assumed in previously published work, the mechanism describing this link appears to be somewhat different from the one postulated previously. Several extensions and directions for future work are also discussed.

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