A Threshold-Satisfying Competitive Location Model

In this paper we consider a location model based on the threshold concept. We find the best location such that the probability of revenue falling short of the threshold is minimized. This objective is appropriate when a firm will not survive if its revenue falls below a known threshold. A new store is to be located. Demand is not deterministic but rather has a statistical distribution. We seek the location at which the probability that the revenue (expressed as market share attracted by the new store) is below a given threshold is minimized. The model is formulated and solved, and computational results are given.     

Analysis of a Distribution of Point Events Using the Network‐Based Quadrat Method

This study proposes a new quadrat method that can be applied to the study of point distributions in a network space. While the conventional planar quadrat method remains one of the most fundamental spatial analytical methods on a two‐dimensional plane, its quadrats are usually identified by regular, square grids. However, assuming that they are observed along a network, points in a single quadrat are not necessarily close to each other in terms of their network distance. Using planar quadrats in such cases may distort the representation of the distribution pattern of points on a network. The network‐based units used in this article, on the other hand, consist of subsets of the actual network, providing more accurate aggregation of the data points along the network. The performance of the network‐based quadrat method is compared with that of the conventional quadrat method through a case study on a point distribution on a network. The χ² statistic and Moran's I statistic of the two quadrat types indicate that (1) the conventional planar quadrat method tends to overestimate the overall degree of dispersion and (2) the network‐based quadrat method derives a more accurate estimate on the local similarity. The article also performs sensitivity analysis on network and planar quadrats across different scales and with different spatial arrangements, in which the abovementioned statistical tendencies are also confirmed.     

SANET: A Toolbox for Spatial Analysis on a Network

This article shows a geographical information systems (GIS)-based toolbox for analyzing spatial phenomena that occur on a network (e.g., traffic accidents) or almost along a network (e.g., fast-food stores in a downtown). The toolbox contains 13 tools: random point generation on a network, the Voronoi diagram, the K -function and cross K -function methods, the unconditional and conditional nearest-neighbor distance methods, the Hull model, and preprocessing tools. The article also shows a few actual analyses carried out with these tools.