Location-Allocation equations

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11-03-2016 09:21 AM
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New Contributor II

Hi everyone,

Are the governing equations for the location-allocation tool available on official ArcGIS (or related) sources?

I'd like to see the math behind, not really the script.

Thank you very much.

Alessandro

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MVP Esteemed Contributor

There is reference to Algorithms used by the ArcGIS Network Analyst extension—Help | ArcGIS for Desktop 

Which for your case ... Algorithms used by the ArcGIS Network Analyst extension—Help | ArcGIS for Desktop 

which cites 

The location-allocation solver starts by generating an origin-destination matrix of shortest-path costs between all the facilities and demand point locations along the network. It then constructs an edited version of the cost matrix by a process known as Hillsman editing. This editing process enables the same overall solver heuristic to solve a variety of different problem types. The location-allocation solver then generates a set of semirandomized solutions and applies a vertex substitution heuristic (Teitz and Bart) to refine these solutions creating a group of good solutions. A metaheuristic then combines this group of ....

Since I knew I had heard this before and that the actual references weren't in the help.... this brought me back to a page that gives them from  Jay Sandhu a more authoritive reference.

Algorithm used by location-allocation (Maximize Coverage problem type) 

But I will copy a portion of his response for posterity.

"....

Here is a reference to the original paper by Ed Hillsman:
Hillsman, E.L. (1984). The p-median structure as a unified linear model for location-allocation analysis. Environment and Planning A, 16 (3), 305-318

And here is another researcher using a similar approach:
http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.26.4638&rep=rep1&type=pdf

..."