Does Euclidean distance work well when the p-median model is applied in rural areas?

The p-median model is used to locate P centers to serve a geographically distributed population. A cornerstone of such a model is the measure of distance between a service center and demand points, i.e. the location of the population (customers, pupils, patients, and so on). Evidence supports the current practice of using Euclidean distance. However, we find that the location of multiple hospitals in a rural region of Sweden with a non-symmetrically distributed population is quite sensitive to distance measure, and somewhat sensitive to spatial aggregation of demand points.

[1]  O. Kariv,et al.  An Algorithmic Approach to Network Location Problems. II: The p-Medians , 1979 .

[2]  James R. Evans,et al.  Aggregation and Disaggregation Techniques and Methodology in Optimization , 1991, Oper. Res..

[3]  Gerard Rushton,et al.  Applications of location models , 1990 .

[4]  Timothy J. Lowe,et al.  On worst-case aggregation analysis for network location problems , 1993, Ann. Oper. Res..

[5]  Mark S. Daskin,et al.  Network and Discrete Location: Models, Algorithms and Applications , 1995 .

[6]  Oded Berman,et al.  Flow intercepting spatial interaction model: a new approach to optimal location of competitive facilities , 1998 .

[7]  Bhaba R. Sarker,et al.  Discrete location theory , 1991 .

[8]  Alan T. Murray,et al.  The Influence of Data Aggregation on the Stability of p-Median Location Model Solutions , 2010 .

[9]  F. Benjamin Zhan,et al.  Shortest Path Algorithms: An Evaluation Using Real Road Networks , 1998, Transp. Sci..

[10]  Trevor S. Hale,et al.  Location Science Research: A Review , 2003, Ann. Oper. Res..

[11]  L Bach,et al.  The Problem of Aggregation and Distance for Analyses of Accessibility and Access Opportunity in Location-Allocation Models , 1981 .

[12]  S. L. Hakimi,et al.  Optimum Locations of Switching Centers and the Absolute Centers and Medians of a Graph , 1964 .

[13]  Timothy J. Lowe,et al.  Aggregation error for location models: survey and analysis , 2009, Ann. Oper. Res..

[14]  Edsger W. Dijkstra,et al.  A note on two problems in connexion with graphs , 1959, Numerische Mathematik.

[15]  Richard L. Church,et al.  COBRA: A New Formulation of the Classic p-Median Location Problem , 2003, Ann. Oper. Res..

[16]  G. Meek Mathematical statistics with applications , 1973 .

[17]  E. Hillsman,et al.  Errors in measuring distances from populations to service centers , 1978 .

[18]  S. L. HAKIMIt AN ALGORITHMIC APPROACH TO NETWORK LOCATION PROBLEMS. , 1979 .

[19]  Pierre Hansen,et al.  The p-median problem: A survey of metaheuristic approaches , 2005, Eur. J. Oper. Res..