On Insensitivities in Urban Redistricting and Facility Location

by Richard C. Larson, K. A. Stevenson

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The expected response time of vehicles, dispatched from fixed facilities to spatially distributed incidents, is shown to be insensitive to substantial changes in facility locations or response district design. Repositioning a set of randomly located facilities so that they are optimally located reduces mean response time by no more than 25 percent. Analysis of simple two-facility models shows, in addition, that wide variations in the position of one facility imply relatively small variations in the position of the second facility for the minimization of mean response time. Accordingly, it is suggested that redistricting and facility location based on crude assumptions coupled with an awareness of the heuristic properties illustrated by simple analytic models may yield mean response times very near the minimum possible. (See also R-531, R-532, R-567.)

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