Available with Business Analyst license.

Creating territories from centers of density allows you to create territories without seed points. You can build territories in a new market where you have minimal knowledge, with no brick-and-mortar locations to start. This option will search territory centers near most dense places in the base layer and create territories from found centers. Centers of density can be found using spatial locations of features in a base layer only or in combination with some attribute, such as population or diversity.

Spatial locations are the centers of geographic objects, such as centers of ZIP Code polygons. The clustering algorithm analyzes the density of these center points and forms clusters from points with the higher density value. Then centers of these clusters are processed to create the desired number of territory centers.

The use spatial locations only command uses actual distances between center points for calculating the density value. Values of attributes are not applied in this case.

The use spatial locations and summary attribute command uses a modified formula for distance calculation:

Modified Distance = Distance / Density Coefficient

Where Density Coefficient = (Value of attribute from Feature 1 + Value of attribute from Feature 2) / 2;

This formula means that features with bigger values of attributes are closer to each other.

As a sample use case, suppose you create territories using an income summary attribute. A few families with an ordinary income live in a 10-square-mile area. In this case, the territory will not be created because the area is too large for a small number of families, and their income is ordinary. Conversely, consider a different area with the same geographic size and same number of families, but with large incomes. The territory will be created in this case because the calculated density value takes into account their large income.

## How Territories are Created from Centers of Density

### Source data analysis

In this phase, the base layer feature centers are analyzed to calculate the average density of the layer.

### Density clusters calculation

The algorithm searches groups of feature centers with density more than the average of the whole layer density. This density creates the clusters.

### Calculation of territory centers based on density clusters

For each density cluster, a calculated weight is based on balancing and capacity variables of the density cluster features. The density cluster centers are processed with help of the "k-means" algorithm accounting for the clusters weight. K-means finds the cluster's desired number of territory centers. Using the weight of clusters helps locate territory centers in positions most suitable to create equally balanced territories.

## Optimal Number of Territories Calculation

With Territory Design you can create a solution with territories which can be optimally chosen depending on the specified restrictions.

### Optimal by Distance constraints

Optimal Number = Current Territory Extent Area / Maximum area of territory (pi * Maximum Distance ^ 2)

If a Territory Extent is not set, the area of the entire base layer will be used.

### Optimal by Capacity constraints

Formula:

_{where N – optimal number of territories, Sum k – summary value of kth variable at specified or max extent, Capacity k – value of capacity of kth variable, Tolerance k – value of tolerance of kth variable (from 0 to 0,99). }

Algorithm:

- Calculate the summary value for each variable in the specified or the max area extent.
- Find the optimal number of territories for each variable (sum/variable value).
- Calculate the weight of each variable based on the tolerance value (tolerance shows importance of variable, less tolerance - more important variable).
- Calculate the average optimal number using variable weight.