Abstract
Spatial operations research problems seek “best” locations, often points of minimum aggregate weighted distance, requiring georeferenced data as input. Frequently maps of such data are incomplete, with holes in their geographic distributions. Spatial statistical procedures are available to complete these data sets with best estimates of the missing values. Impacts such imputations have on 2-median facility location–allocation solutions are explored. The sampling distribution of the spatial mean and standard distance of these medians are studied. Population density is used as the weight attribute in determining location-allocation solutions because it can be accurately described with a relatively simple spatial statistical model.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Casillas, P. (1987). “Data Aggregation and the p-Median Problem in Continuous Space.” In A. Ghosh and G. Rushton (eds.), Spatial Analysis and Location–Allocation Models. New York: Van Nostrand-Reinhold, pp. 327–344.
Current, J. and D. Schilling. (1987). “Elimination of Source A and B Errors in p-Median Problems.” Geographical Analysis 19, 95–110.
Gilbert, R. (1987). Statistical Methods for Environmental Pollution Monitoring. New York: Van Nostrand-Reinhold.
Griffith, D. (1992). “Estimating Missing Values in Spatial Urban Census Data.” The Operational Geographer 10(2), 23–26.
Griffith, D. (1997). “Using Estimated Missing Spatial Data in Obtaining Single Facility Location–Allocation Solutions.” L'Espace Géographique 26, 173–182.
Griffith, D. and A. Can. (1995). “Spatial Statistical/Econometric Versions of Simple Urban Population Density Models.” In S. Arlinghaus (ed.), Practical Handbook of Spatial Statistics. Boca Raton, FL: CRC Press, pp. 231–249.
Griffith, D., R. Haining, and R. Bennett. (1989). “Statistical Analysis of Spatial Data in the Presence of Missing Observations: A Methodological Guide and an Application to Urban Census Data.” Environment & Planning A 21, 1511–1523.
Haining, R., D. Griffith, and R. Bennett. (1984). “A Statistical Approach to the Problem of Missing Spatial Data Using a First-Order Markov Model.” The Professional Geographer 36, 338–345.
Hakimi, S. (1965). “Optimum Distribution of Switching Centers in a Communications Network and Some Related Graph-Theoretic Problems.” Operations Research 13, 462–475.
Hillsman, E. and R. Rhoda. (1978). “Errors in Measuring Distances from Populations to Service Centers.” Annals of Regional Science 12, 74–88.
Hodgson, J. (1991). “Stability of the p-Median Model under Induced Data Error.” INFOR 29, 167–183.
Hodgson, J. and J. Oppong. (1989). “Some Efficiency and Equity Effects of Boundaries in Location–Allocation Models.” Geographical Analysis 21, 167–178.
Kuhn, H. and R. Kuenne. (1962). “An Efficient Algorithm for the Numerical Solution of the Generalized Weber Problem in Spatial Economics.” Journal of Regional Science 4, 21–34.
McLachlan, G. and T. Krishnan. (1997). The EM Algorithm and Extensions. New York: Wiley.
Ohsawa, Y., T. Koshizuka, and O. Kurita. (1991). “Errors Caused by Rounded Data in Two Simple Facility Location Problems.” Geographical Analysis 23, 56–73.
Ostresh, L. (1973a). “ALTERN –Heuristic Solution to the m-Center Location–Allocation Problem.” In G. Rushton, M. Goodchild, and L. Ostresh (eds.), Computer Programs for Location–Allocation Problems. Iowa City, IA: University of Iowa, Department of Geography, Monograph No. 6, pp. 55–66.
Ostresh, L. (1973b). “MULTI –Exact Solution to the m-Center Location–Allocation Problem.” In G. Rushton, M. Goodchild, and L. Ostresh (eds.), Computer Programs for Location–Allocation Problems. Iowa City, IA: University of Iowa, Department of Geography, Monograph No. 6, pp. 29–54.
Ostresh, L. (1973c). “TWAIN –Exact Solution to the Two Source Location–Allocation Problem.” In G. Rushton, M. Goodchild, and L. Ostresh (eds.), Computer Programs for Location–Allocation Problems. Iowa City, IA: University of Iowa, Department of Geography, Monograph No. 6, pp. 15–28.
Ostresh, L. (1973d). “WEBER –Exact Solution to the One Source Location–Allocation Problem.” In G. Rushton, M. Goodchild, and L. Ostresh (eds.), Computer Programs for Location–Allocation Problems. Iowa City, IA: University of Iowa, Department of Geography, Monograph No. 6, pp. 1–14.
Richard, D., H. Beguin, and D. Peters. (1990). “The Location of Fire Stations in a Rural Environment: a Case Study.” Environment and Planning A 22, 39–52.
Weiszfeld, E. (1937). “Sur le point pour lequel la somme des distances de n points donnes est minimum.” Tohoku Mathematical Journal 43, 355–386.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Griffith, D.A. Using Estimated Missing Spatial Data with the 2-Median Model. Annals of Operations Research 122, 233–247 (2003). https://doi.org/10.1023/A:1026106825798
Issue Date:
DOI: https://doi.org/10.1023/A:1026106825798