Distance measure and the \(p\)-median problem in rural areas
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The \(p\)-median model is used to locate \(P\) facilities to serve a geographically distributed population. Conventionally, it is assumed that the population patronizes the nearest facility and that the distance between the resident and the facility may be measured by the Euclidean distance. Carling et al. (Ann Oper Res 201(1):83–97, 2012) compared two network distances with the Euclidean in a rural region with a sparse, heterogeneous network and a non-symmetric distribution of the population. For a coarse network and \(P\) small, they found, in contrast to the literature, the Euclidean distance to be problematic. In this paper we extend their work by use of a refined network and study systematically the case when \(P\) is of varying size (1–100 facilities). We find that the network distance give almost as good a solution as the travel-time network. The Euclidean distance gives solutions some 2–13 % worse than the network distances, and the solutions tend to deteriorate with increasing \(P\). Our conclusions extend to intra-urban location problems.
KeywordsDense network Location model Optimal location Simulated annealing Travel-time Urban areas
Financial support from the Swedish Retail and Wholesale Development Council is gratefully acknowledged.
- Al-khedhairi, A. (2008). Simulated annealing metaheuristic for solving p-median problem. International Journal of Contemporary Mathematical Sciences, 3(28), 1357–1365.Google Scholar
- Han, M., Håkansson, J., & Rebreyend, P., (2012). How does the use of different road networks effect the optimal location of facilities in rural areas? Working papers in transport, tourism, information technology and microdata analysis, Dalarna university, 2012:02.Google Scholar
- Han, M., Håkansson, J., Rebreyend, P., (2013). How do different densities in a network affect the optimal location of service centers? Working papers in transport, tourism, information technology and microdata analysis, Dalarna university, 2013:15.Google Scholar
- Handler, G. Y., & Mirchandani, P. B. (1979). Location on networks: Theorem and algorithms. Cambridge, MA: MIT Press.Google Scholar