Trying to Grow Regions in Spatial Analyst?

Discussion created by timmul72 on May 15, 2014
I am working on a raster-based accessibility problem in which I have 3 layers.  One is a points location that we will create regions around.  The second is a travel-time raster the represents the amount of time it takes to travel through the pixel and the third represents the number of people that live within each pixel (derived from population density).

I am working with a social geographer/political scientist to find "travel sheds" that are constrained by population for each of the points.  I have created travelsheds already, but in some instances, points are located near each other and one travel shed is extremely small.  In that case, I want them to grow in opposite directions, as each will "gobble" up population until it exceeds my threshold so that each travelshed has approximately the same number of people.  In essence, I want to assign a pixel a "basin" that is closest to a point, but has not exceeded the population constraint.  Otherwise, it will be assigned to the next closest point that hasn't satisfied the population criteria, etc... 

Can anyone think of any ways to do this in Spatial Analyst?  I'm stuck at the part where I am trying to constrain by population.  I've tried playing with a "people-minute" raster, but not sure how that bring that back to a polygon shape.  I'm also familiar enough with Python and R if this can't be done in Spatial Analysis.  Any ideas that would point me in the right direction would be greatly appreciated.  I'm also not afraid to try new things if there is something out there that can easily do this.  Thank you.