Connecting Points to Spatial Networks: Effects on Discrete Optimization Models

To accommodate network allocation, population polygons are frequently transformed into singular, weighted centroids which are then integrated into the network either by snapping each centroid to the nearest network segment or by generating an artificial connector that becomes part of the network. In this article, an investigation of the connection method of network allocation is undertaken with two primary foci: (1) how the density of centroid connectors effects travel cost along the network; and (2) how the algorithms utilized to determine the placement of connectors are affected by the density of connectors. We hypothesize that both issues have an effect on network travel cost and, therefore, on network-based modeling. These hypotheses are tested on three nested spatial networks in the New England region of the United States. Two fundamental facility location models, the p-median problem, and p-center problem, are solved at each spatial extent while varying the density of connectors from one to four. When generating more than one connector thought must be given to the method of connection, the angle of dispersion, the acceptable tolerance of connector length, segment crossing, and saturated connectivity. A novel and thorough framework is proposed to address these concerns.