# How does cost allocation work?

Why, when I use the cost allocation function of Spatial Analyst, is space not allocated in all input source locations (as shown in image below)? In particular, the input raster has 18 spots while the cost function allocates only 14 spaces. Can I force the function to allocate space in all input source locations? and how?

Full-sized image here: http://i.stack.imgur.com/5k1Od.jpg

• Do you have an image of your cost raster? That would help with this question. – blord-castillo Sep 28 '11 at 12:19
• How do you know only 14 regions appear in the allocation? Is it by inspecting the attribute table or only by looking at the map? (It's possible the map is deceptive; for instance, some regions could be so small that they are covered by the point symbols.) Also, are you sure the 18 point locations were accurately converted to grid format for input to cost allocation? Sometimes points disappear in this process (but ArcGIS rarely emits a message to that effect). Here, it looks like points 21, 93, 109, and 181 were not used. – whuber Sep 28 '11 at 15:19
• 1. I have uploaded the cost raster above (2nd figure). – Demetris Sep 28 '11 at 17:54
• 2. I had a look in the attribute table and clrealy there are only 14 regions. Yes, I am sure the source file has 18 locations as shown in Figure 1. Yes, points 21, 93, 109 and 181 were not actually used and I wonder why? – Demetris Sep 28 '11 at 17:56
• Yes. I have converted the source layer, that is, points to raster. You may see the atrribute table I have uploaded above with the 18 points. – Demetris Sep 29 '11 at 18:21

According to the documentation from the ArcGIS site, Cost Allocation

Calculates for each cell its nearest source based on the least accumulative cost over a cost surface.

You ended up with only 14 spaces because no cells have those four sources as their nearest source in terms of accumulated cost (as indicated by your cost raster). Had this been simple geometric proximity allocation, then you would have 18 spaces. However, nearness here is expressed in terms of accumulated travel cost. You learn more about how the computation is done here.

I think what you expected were Thiessen polygons.

To address @whuber's points, I think we need the original data sources ( input rasters, cost rasters ) to do a more specific analysis. Tried to replicate the analysis but as I only had the source points as opposed to the original raster, my results weren't the same. I got the following cost allocation raster:

• These are intriguing claims, but let's get specific: could you explain how it is possible for any valid cost raster to allocate the cell at point "5" (in the question) to point "93"? Assuming all costs are positive, the cost to get to point 93 must be positive, whereas the cost for the cell at point 5 (presumably) is zero. The ArcGIS help page you quote here sheds no light on this. (Note--as documented in a comment to the question--that the costs appear to be constant, or nearly so.) – whuber Sep 16 '12 at 19:06
• I think I'm gonna need the original data for that. What we have so far are the point sources and the cost raster. The OP has said it was an input raster. The point sources make for a rather poor approximation. – R.K. Sep 17 '12 at 0:45