Optimal weighted ℓ_<i>p</i></i> norm parameters for facilities layout distance characterizations

Abstract

<p>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 ℓ_p 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.</p>