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Creating optimal patrol areas using the P-median model

Andrew Palmer Wheeler (School of Economic Political and Policy Sciences, Program in Criminology and Criminal Justice, University of Texas at Dallas, Richardson, Texas, USA)

Policing: An International Journal

ISSN: 1363-951X

Article publication date: 14 August 2018

Issue publication date: 23 May 2019




The purpose of this paper is to illustrate the use of the p-median model to construct optimal patrol areas. This can improve both time spent traveling to calls, as well as equalize call load between patrol areas.


The paper provides an introduction to the use of integer linear programs to create optimal patrol areas, as many analysts and researchers in the author’s field will not be familiar with such models. The analysis then introduces a set of linear constraints to the p-median problem that are applicable to police agencies, such as constraining call loads to be equal and making patrol areas geographically contiguous.


The analysis illustrates the technique on simplified simulated examples. The analysis then demonstrates the utility of the technique by showing how patrol areas in Carrollton, TX can be made both more efficient and equalize the call loads given the same number of patrol beats as currently in place.


Unlike prior applications of creating patrol areas, this paper introduces linear constraints into the p-median problem, making it much easier to solve than programs that have non-linear or multiple objective functions. Supplementary code using open source software is also provided, allowing other analysts or researchers to apply the model to their own data.



The author would like to thank the Carrollton Police Department and in particular Cdr. Andrew Horn and Chief Derek Miller for the opportunity to collaborate on this project, data and code to replicate the findings can be obtained from


Wheeler, A.P. (2019), "Creating optimal patrol areas using the P-median model", Policing: An International Journal, Vol. 42 No. 3, pp. 318-333.



Emerald Publishing Limited

Copyright © 2018, Emerald Publishing Limited

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