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BackgroundDecision making in the health area usually involves several factors, options and data. In addition, it should take into account technological, social and spatial aspects, among others. Decision making methodologies need to address this set of information , and there is a small group of them with focus on epidemiological purposes, in particular Spatial Decision Support Systems (SDSS).MethodsMakes uses a Multiple Criteria Decision Making (MCDM) method as a combining rule of results from a set of SDSS, where each one of them analyzes specific aspects of a complex problem. Specifically, each geo-object of the geographic region is processed, according to its own spatial information, by an SDSS using spatial and non-spatial data, inferential statistics and spatial and spatio-temporal analysis, which are then grouped together by a fuzzy rule-based system that will produce a georeferenced map. This means that, each SDSS provides an initial evaluation for each variable of the problem. The results are combined by the weighted linear combination (WLC) as a criterion in a MCDM problem, producing a final decision map about the priority levels for fight against a disease. In fact, the WLC works as a combining rule for those initial evaluations in a weighted manner, more than a MCDM, i.e., it combines those initial evaluations in order to build the final decision map.ResultsAn example of using this new approach with real epidemiological data of tuberculosis in a Brazilian municipality is provided. As a result, the new approach provides a final map with four priority levels: “non-priority”, “non-priority tendency”, “priority tendency” and “priority”, for the fight against diseases.ConclusionThe new approach may help public managers in the planning and direction of health actions, in the reorganization of public services, especially with regard to their levels of priorities.

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Given a solid T , represented by a compact set in R 3 , the aim of this work is to find a covering of T by a finite set of spheres of different radii. Some level of intersection between the spheres is necessary to cover the solid. Moreover, the volume occupied by the spheres on the outside of T is limited. This problem has an application in the planning of a radio-surgery treatment known by Gamma Knife and can be formulated as a non-convex optimization problem with quadratic constraints and linear objective function. In this work, two new linear mathematical formulations with binary variables and a hybrid method are proposed. The hybrid method combines heuristic, data mining and an exact method. Computational results show that the proposed methods outperform the ones presented in the literature.Mathematics Subject Classification. 90C10.

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