Location-Allocation with maximum supply constraint and automatic site selection

Question

Hey, 
 
I' m working here on a service allocation problem.

I am constricted by a certain number of potential facility locations (9) and a maximum capacity of each facility (100 connected demand points).  In total I have 500 demand points.  Now, I want to automatically select  5 optimal facility locations (out of the 9 potential locations), so that each facility has 100 demand points allocated. The selection should minimize the total travel distance between the facilities and demand points. 
 
As far as I found out, there is no way to do this with the network analyst, as there can be no max. capacity for facilities defined in the location-allocation tool. Is there any script or work-around that could do the job for me?
 
Thanks for your help and best regards, 
 
Rafael

JaySandhu · Answer

Is there no tool which can work with network distances (e.g. from an OD-Cost Matrix) instead of direct distances?

The partitioning tools do not use distance at all! And thus cannot be enhanced by network distances. It is based on a space-filling Peano curve.Can you now me if it can at least solve my kind of problem? Than I would get into getting it to work.

The Allocation tools work for the case when the facility locations are known (for example existing school locations) and they have a capacity and there is a list of demand points (e.g., school going children) that need to be "allocated" to these existing locations honoring their capacity. These scripts will not tell you where to locate your facilities.

The only tool that will tell you where to place the facilities is Location-Allocation and in version 10 it does not have the capability to honor capacity. That has been added in 10.1 pre-release which will be out shortly.

You can look at location-allocation literature and see how to formulate it as a Linear Programming problem and then use the Allocation tool approach to solve it by computing the OD in ArcGIS, exporting the OD out to the LP package. But be warned that this approach will take time to develop/test and it will only solve small problems and may take a long time solving to give a good solution.

Jay Sandhu

RS · Answer

Dear Jay,

your hint works well for as approximation for me. 
Is there no tool which can work with network distances (e.g. from an OD-Cost Matrix) instead of direct distances?

I downloaded the Allocation Tools (http://resources.arcgis.com/gallery/file/geoprocessing/details?entryID=C4E79AE3-1422-2418-88B2-008CC5F9D24F), it is not working right now. 
Can you now me if it can at least solve my kind of problem? Than I would get into getting it to work.

Thanks for your advice

Rafael

JaySandhu · Answer

If you simply want a solution then take a look at the partitioning tools:
http://resources.arcgis.com/gallery/file/Geoprocessing-Model-and-Script-Tool-Gallery/details?entryID=6057ADFA-1422-2418-A056-8D337B093947

Keep in mind that this does not use network analyst or location-allocation. But will give you a specified number of clusters of a certain size.

Jay Sandhu