The district02.lng Model

Districting/Clustering example in LINGO

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Partition or group a set of small population units into a specified number of larger clusters/districts/territories, so that each cluster looks good according to various measures. This problem arises in the design of political districts, sales territories, and other clustering applications. This model considers six features/measures: 1) Size Similarity: the population assigned to each cluster should be close to the same for all clusters, 2) Closeness: the average distance of the units in a cluster from the cluster center should be small, e.g., if transport costs are important, 3) Compactness: The total boundary length of the clusters should be small. A unitless measure of compactness, called the Polsby-Popper score, is the ratio 4*PI*Area/Perimeter^2. For the most compact shape, a circle, this ratio is 1. You cannot tile any area with circles, the best you can do is regular hexagons, for which this ratio is . 4) Connected: Each cluster should be connected geographically, i.e., for any two units in the same cluster, there must be a path connecting them. In network terminology, each district contains a spanning tree, 5) Feature Similarity: The maximum width of cluster by some measure, e.g., time zone difference, should be small, 6) Gerrymandering feature: If each unit has some fraction of its population belonging to our political party, we want to have a large number of clusters in which our party has the majority,

Keywords:

Assignment | Plant Location | Cluster Analysis | Location | Compactness | Connectedness | Districting | Gerrymander | Political Districting | Sales Districting | Territory Design | LINGO | Polsby | Popper |