Maximal covering, Backup covering, Optimization, Geographic information systems, Police patrol areas, Police beats,

No abstract

Network data structures were one of the earliest representations in geographic information systems (GIS), and network analysis remains one of the most significant and persistent research and application areas in geographic information science (GIScience). Network analysis has a strong theoretical basis in the mathematical disciplines of graph theory and topology, and it is the topological relationships inherent in networks that led to revolutionary advances in GIS data structures. Networks can represent an alternative datum for geo-location in the context of linear referencing and support a set of tools for graphical display known as dynamic segmentation. Many network location problems are among the most difficult to solve in terms of their combinatorial complexity and, therefore, provide both a challenge and an opportunity for GIScience researchers. Because elements of network analysis appear in a wide range of academic disciplines-from physics, to sociology, to neurobiology-there are ample opportunities for interdisciplinary investigations of emerging research topics.

Objective: The purpose of the study was to examine geographic relationships of nutritional status (BMI), including underweight, overweight and obesity, among Kenyan mothers and children. Design: Spatial relationships were examined concerning BMI of the mothers and BMI-for-age percentiles of their children. These included spatial statistical measures of the clustering of segments of the population, in addition to inspection of co-location of significant clusters. Setting: Rural and urban areas of Kenya, including the cities of Nairobi and Mombasa, and the Kisumu region. Subjects: Mother-child pairs from Demographic and Health Survey data including 1541 observations in 2003 and 1592 observations in 2009. These mother-child pairs were organized into 399 locational clusters. Results: There is extremely strong evidence that high BMI values exhibit strong spatial clustering. There were co-locations of overweight mothers and overweight children only in the Nairobi region, while both underweight mothers and children tended to cluster in rural areas. In Mombasa clusters of overweight mothers were associated with normal-weight children, while in the Kisumu region clusters of overweight children were associated with normal-weight mothers. Conclusions: These findings show there is geographic variability as well as some defined patterns concerning the distribution of malnutrition among mothers and children in Kenya, and suggest the need for further geographic analyses concerning the potential factors which influence nutritional status in this population. In addition, the methods used in this research may be easily applied to other Demographic and Health Survey data in order to begin to understand the geographic determinants of health in low-income countries.

One of the defining objectives in location science is to maximize dispersion. Facilities can be dispersed for a wide variety of purposes, including attempts to optimize competitive market advantage, disperse negative impacts, and optimize security. With one exception, all of the extant dispersion models consider only one type of facility, and ignore problems where multiple types of facilities must be located. We provide examples where multiple-type dispersion is appropriate and based on this develop a general class of facility location problems that optimize multiple-type dispersion. This family of models expands on the previously formulated definitions of dispersion for single types of facilities, by allowing the interactions among different types of facilities to determine the extent to which they will be spatially dispersed. We provide a set of integer-linear programming formulations for the principal models of this class and suggest a methodology for intelligent constraint elimination. We also present results of solving a range of multiple-type dispersion problems optimally and demonstrate that only the smallest versions of such problems can be solved in a reasonable amount of computer time using general-purpose optimization software. We conclude that the family of multiple-type dispersion models provides a more comprehensive, flexible, and realistic framework for locating facilities where weighted distances should be maximized, when compared with the special case of locating only a single type of facility.