Empirical distance functions are used for such purposes as predicting travel distances in a transportation network, estimating the lengths of conductors used in piping and wiring systems, verifying distance data, and formulating location models. It has been previously found that when the reference.axes are correctly rotated, the weighted l, norm is a robust distance predictor. However, a specialized computer program is required to fit this model to a geographical region. In this paper we show how the parameters of the model may be accurately calculated with a standard linear regression program, thus eliminating the need to develop or buy specialized computer software. The method has been verified empirically for several geographical regions.

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The distances used in certain types of industrial, office or street grid layouts are often assumed to be rectangular. Because of the “doubling back” effect caused by finite block and facility sizes, actual distances travelled are often much greater than indicated by the l1 norm. In this study the weighted lp norm is fitted to a certain commonly occurring class of layout patterns. The optimal best-fit parameters are reported in addition to other observations which should be useful to users of distance models. The results give strong support for the use of the l1 norm in determining optimal facility locations when travel distances are rectangular and doubling back occurs. However, the l1 norm is not appropriate for modelling actual travel distances under the same circumstances.

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A procedure for obtaining a facilities scatter diagram within a rectangular boundary is developed using a multifacility location model. This method gives favorable computational results and has the advantage over other scatter diagram methods of being able to accommodate fixed facility locations. Examples illustrate how this method can be used by a designer/analyst either as a one‐step algorithm or iteratively to build a layout.