ArcGIS raster-based districting for equal population districts: cost allocation?

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My goal is to define 13 starting points as centers from which districts will "spread out" across a raster (containing population data for each cell) until each district contains equal population AND all cells have been "gobbled". Cost allocation almost does this, but the resultant districts don't have equal populations ("count" in the table). Is there a built-in way to do something like this in ArcGIS 10.2? Or would I need to create a custom Python script -- and if so, are there any resources that would help me get started?



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