Gerard Rushton

A MORE EFFICIENT HEURISTIC FOR SOLVING LARGE P-MEDIAN PROBLEMS

The Teitz and Bart (1968) vertex substitution heuristic is more robust than competing algorithms and yields solutions with properties that are necessary, but not sufficient, for a global optimum solution. All documented implementations of this algorithm, however, use a naive spatial search procedure, whereas a more informed spatial search procedure, requiring considerably less computation to solve any given problem, is possible. An algorithm incorporating this new search procedure, called the global/regional interchange algorithm, is described. As problem size increases, proportionally larger reductions in processing costs occur.

Strategies for Solving Large Location-Allocation Problems by Heuristic Methods

Solution techniques for location-allocation problems usually are not a part of microcomputer-based geoprocessing systems because of the large volumes of data to process and store and the complexity of algorithms. In this paper, it is shown that processing costs for the most accurate, heuristic, location-allocation algorithm can be drastically reduced by exploiting the spatial structure of location-allocation problems. The strategies used, preprocessing interpoint distance data as both candidate and demand strings, and use of them to update an allocation table, allow the solution of large problems (3000 nodes) in a microcomputer-based, interactive decisionmaking environment. Moreover, these strategies yield solution times which increase approximately linearly with problem size. Tests on four network problems validate these claims.

MODELS OF INTRA-URBAN CONSUMER BEHAVIOR AND THEIR IMPLICATIONS FOR CENTRAL PLACE THEORY*

In geography as in other social sciences there has been an unwillingness to show the relevance of empirical findings to established theory.1 This is true of empirical studies of central place systems even though many such studies profess an interest in central place theory. The list of works that attempt to confirm aspects of central place theory is now so long that the profession might expect some rather definitive conclusions to exist concerning the role and the relevance of this theory in the explanation of the locations of cities [4]. We maintain that few such conclusions exist and that those attempts to find properties of central place systems in the real world, as they were described in the classical statements of Losch and Christaller, have not contributed to a scientific evaluation of the role and efficiency of the theory. There are two sets of behavioral postulates in central place theory and, while both have been frequently discussed in the literature, the consequences that would follow if these postulates were different from those assumed by the theorists have been almost totally neglected. One postulate describes the behavior of entrepreneurs. The Losch formulation states that whenever purchasing power equal to or greater than a given threshold for a good exists, an entrepreneur will commence offering the

Geocoding accuracy and the recovery of relationships between environmental exposures and health

BackgroundThis research develops methods for determining the effect of geocoding quality on relationships between environmental exposures and health. The likelihood of detecting an existing relationship – statistical power – between measures of environmental exposures and health depends not only on the strength of the relationship but also on the level of positional accuracy and completeness of the geocodes from which the measures of environmental exposure are made. This paper summarizes the results of simulation studies conducted to examine the impact of inaccuracies of geocoded addresses generated by three types of geocoding processes: a) addresses located on orthophoto maps, b) addresses matched to TIGER files (U.S Census or their derivative street files); and, c) addresses from E-911 geocodes (developed by local authorities for emergency dispatch purposes).ResultsThe simulated odds of disease using exposures modelled from the highest quality geocodes could be sufficiently recovered using other, more commonly used, geocoding processes such as TIGER and E-911; however, the strength of the odds relationship between disease exposures modelled at geocodes generally declined with decreasing geocoding accuracy.ConclusionAlthough these specific results cannot be generalized to new situations, the methods used to determine the sensitivity of results can be used in new situations. Estimated measures of positional accuracy must be used in the interpretation of results of analyses that investigate relationships between health outcomes and exposures measured at residential locations. Analyses similar to those employed in this paper can be used to validate interpretation of results from empirical analyses that use geocoded locations with estimated measures of positional accuracy.

Use of Location-Allocation Models for Improving the Geographical Accessibility of Rural Services in Developing Countries

Improved geographical accessibility to basic services for rural populations is a goal of most governments in developing countries. Yet, only rarely have formal methods for determining optimal locations (location-allocation models) been used as an aid to decisionmaking. The use of location-allocation models in health services development and in regional settlement planning are reviewed and compared to school location planning where these models have not been used. Further research is needed to determine the appropriate objective functions, the roles for modeling in the context of decentralized decisionmaking and the efficiency of past processes of location decisionmaking.

Analyzing Geographic Patterns of Disease Incidence: Rates of Late-Stage Colorectal Cancer in Iowa

This study, using geocodes of the locations of residence of newly diagnosed colorectal cancer patients from the Iowa Cancer Registry, computed continuous spatial patterns of late-stage rates of colorectal cancer in Iowa. Variations in rates in intrahospital service regions were as great as interhospital service regions, shown by analysis of variance tests. Some of the spatial variations observed could be explained, using a general linear regression model on individual-level data, by spatial variations in attributes of individuals and their relationships to health resources. We show how this source of variation can be removed from the original map leaving a new map showing the remaining variation in late-stage rate not explained by these relationships. We argue that it would be more appropriate to organize prevention and control activities targeted at the areas with higher than expected late-stage rates shown on this map. The originality of this approach is in the integration of geocoded data from a cancer registry with methods of spatial analysis that provide considerable geographic detail in the cancer rate while controlling for rate stabilization and reliability due to the small number problem.

Optimizing the size and locations of facilities in competitive multi-site service systems

We propose a multi-site location-allocation model for selecting locations in competitive service systems. Examples are typical franchise systems or retailers with multiple outlets. The proposed objective function maximizes a measure of spatial utility of users subject to constraints on waiting time of users and budget of the multi-site facility owners. The intent is to provide model support in assisting with decisions by one multi-facility owner about locating new sites or closing current sites in the presence of one or more competitors, each of which control several sites. Algorithms and spatial data necessary for solving the problem are described. The model is described in the context of locating bank branches though it is applicable in many other contexts.

Cartographic Displays to Support Locational Decision Making

A functional taxonomy is developed that describes the kinds of maps decision makers can use to evaluate changes in the locations of activities to serve distributed demand. Chorognostic, monoplan, and delta displays can be used for a variety of purposes during all three stages of the decision-making process: problem research and definition, the generation of alternative solutions, and selection of a course of action. Implementations of these display types are described. Finally, the authors argue that in a visual interactive modeling environment, linkages between the objective space of mathematical models and the graphical space of cartographic displays will enable decision makers to select more appropriate analytical models and to intervene and change their decision criteria. These results contribute to improved decision making in complex geographical contexts.

Using software agents to preserve individual health data confidentiality in micro-scale geographical analyses

Confidentiality constraints often preclude the release of disaggregate data about individuals, which limits the types and accuracy of the results of geographical health analyses that could be done. Access to individually geocoded (disaggregate) data often involves lengthy and cumbersome procedures through review boards and committees for approval (and sometimes is not possible). Moreover, current data confidentiality-preserving solutions compatible with fine-level spatial analyses either lack flexibility or yield less than optimal results (because of confidentiality-preserving changes they introduce to disaggregate data), or both. In this paper, we present a simulation case study to illustrate how some analyses cannot be (or will suffer if) done on aggregate data. We then quickly review some existing data confidentiality-preserving techniques, and move on to explore a solution based on software agents with the potential of providing flexible, controlled (software-only) access to unmodified confidential disaggregate data and returning only results that do not expose any person-identifiable details. The solution is thus appropriate for micro-scale geographical analyses where no person-identifiable details are required in the final results (i.e., only aggregate results are needed). Our proposed software agent technique also enables post-coordinated analyses to be designed and carried out on the confidential database(s), as needed, compared to a more conventional solution based on the Web Services model that would only support a rigid, pre-coordinated (pre-determined) and rather limited set of analyses. The paper also provides an exploratory discussion of mobility, security, and trust issues associated with software agents, as well as possible directions/solutions to address these issues, including the use of virtual organizations. Successful partnerships between stakeholder organizations, proper collaboration agreements, clear policies, and unambiguous interpretations of laws and regulations are also much needed to support and ensure the success of any technological solution.

The spatial relationship between infant mortality and birth defect rates in a U.S. city.

The spatial patterns of infant mortality and birth defect rates in the Des Moines, Iowa, urban region are described as a contoured surface based on the punctual kriging of address-matched vital statistics records from The Iowa Department of Public Health. Areas defined as having high rates are shown to be sensitive to the size of the spatial filtering units. There is no correlation between infant mortality and birth defect rates in the region. The significance of areas with high rates is determined by a Monte Carlo simulation procedure. One area of high infant mortality is found in the region, which contrasts with many smaller areas with high birth defect rates in the region. The observed birth defect rate pattern is consistent with the hypothesis that each birth was equally likely to result in a birth defect, while the infant mortality pattern is unlikely to be the result of such an equal likelihood process.