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To link to full-text access for this article, visit this link: http://dx.doi.org/10.1016/j.cor.2006.03.006 Byline: Richard L. Church Abstract: The p-median problem is perhaps one of the most well-known location-allocation models in the location science literature. It was originally defined by Hakimi in 1964 and 1965 and involves the location of p facilities on a network in such a manner that the total weighted distance of serving all demand is minimized. This problem has since been the subject of considerable research involving the development of specialized solution approaches as well as the development of many different types of extended model formats. One element of past research that has remained almost constant is the original ReVelle-Swain formulation [ReVelle CS, Swain R. Central facilities location. Geographical Analysis 1970;2:30-42]. With few exceptions as detailed in the paper, virtually no new formulations have been proposed for general use in solving the classic p-median problem. This paper proposes a new model formulation for the p-median problem that contains both exact and approximate features. This new p-median formulation is called Both Exact and Approximate Model Representation (BEAMR). We show that BEAMR can result in a substantially smaller integer-linear formulation for a given application of the p-median problem and can be used to solve for either an exact optimum or a bounded, close to optimal solution. We also present a methodological framework in which the BEAMR model can be used. Computational results for problems found in the OR_library of Beasley [A note on solving large p-median problems. European Journal of Operational Research 1985;21:270-3] indicate that BEAMR not only extends the application frontier for the p-median problem using general-purpose software, but for many problems represents an efficient, competitive solution approach. Author Affiliation: Department of Geography and The National Center for Geographic Information and Analysis, University of California at Santa Barbara, Santa Barbara, CA 93106-4060, USA

To link to full-text access for this article, visit this link: http://dx.doi.org/10.1016/j.cor.2006.03.004 Byline: Alan T. Murray (a), Morton E. O'Kelly (a), Richard L. Church (b) Abstract: Service coverage is an often utilized concept in location modeling. Whether it be evaluating existing facilities or planning for new services, an underlying goal in many planning efforts is providing at least a minimal level of service coverage to an entire region. Examples include locating emergency medical services so as to ensure acceptable response times or siting Doppler radar stations to monitor evolving weather conditions. A challenge in addressing such problems has been how to represent a study region in a digital (or mathematical) environment. Historically, the approach taken has been to represent a region as an irregular pattern of points. These points typically correspond to centroids (or centers) of neighborhoods, towns, administrative units or census boundaries and summarize population or other service demand characteristics used in location models. A related alternative has been to represent a region as a regular pattern of points. The proliferation of geographic information systems (GIS), and the spatial data they manage, suggests that such representations may be overly simplistic in some circumstances. Further, there is increasingly an attempt to incorporate greater richness in traditional location modeling approaches. In this paper we explore coverage modeling of a region. An application focusing on siting emergency warning sirens in an urban area is used to evaluate the effectiveness of alternative coverage modeling approaches. Author Affiliation: (a) Department of Geography, The Ohio State University, 1036 Derby Hall, 154 North Oval Mall, Columbus, OH 43210, USA (b) Department of Geography, University of California at Santa Barbara, Santa Barbara, California 93106, USA