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,


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