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Creating wedge-shaped territories

Juanette

Good morning, I am trying to create new territories for our inspectors based on the number of locations to be inspected. Our office is centrally located in the county. We are wanting to have wedge-shaped territories radiating from our office, like pieces of a pie. Any suggestions on how to have the GIS assist with the division?

Thanks,

Juanette

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Juanette

David Bollinger, I am updating this distribution which was discussed back in 2016. As you suggested, I am looking at using values instead of count. You mentioned you had done so for a 2010 Supervisorial Redistricting. If by some chance you happen to still have your script, I would love to have a look at it. I haven't touched python since 2016 and am just now working on my script and appreciate any assistance. I am interested in both the using values and adjusting the starting angles.

The gang on this site were incredibly helpful in 2016! Xander Bakker‌, Your script worked beautifully with some personal tweaks. You have no idea how grateful I am to you.

2016 EH facility distribution. The darker wedges are for supervisors and have half the number of facilities. Our office is near the center, where the wedges join.

XanderBakker

The process you are describing is what my script is doing. The "fudge factor", you mention is the variable "tol" in my script.

tol = 3 # a tolerance value (will stop if current value >= search value - tolerance)

DavidBollinger

aside, fwiw (and replying to self): we did exactly as described above to generate requested "what if radial" scenarios for 2010 Supervisorial Redistricting, using Census centroids as the sites and their summed population as the value (ie, rather than number of included sites, the value of all included sites). we did it a couple of times using various "starting angles" (which occasionally had dramatic influence on final result), but they were all just "curiosities" - they all failed other conditions required of those particular boundaries, though it was pretty easy to satisfy the equal-within-tolerance distributions.

DavidBollinger

equal-angle and equal-area approaches are useful first approximations, but there's a "relatively easy" way to approximate what is probably truly desired (equal-distribution) via iterative methods, requiring only some small modifications if given a script like the one you posted earlier.

finding a set of N radial dividing lines that would exactly equally divide a population P of sites would be a non-trivial optimization problem. however, if we're already admitting straight-line travel distance and other such approximations, then perhaps something like the following approach would suffice, fwiw: (only intent is slight improvement of distribution versus a rigid set of two_pi/N angles, not "perfection")

we are given N and P, (or, at least, the OP knows those values), so we also know ideal P/N (aka "sites per inspector"). now let's also define a bit of a "fudge factor", say 5%? around that ideal value, and consider the value P/N-F.

now iterate your wedge angles one degree at a time (or some other small amount - there's a speed/accuracy trade-off impleid here) and keep track of the total accumulated angle. create a "test" wedge at the current total accumulated angle, and count its contents. if within tolerance of the fudge factor, accept it and reset your total; if not, continue to next iteration and test again with a slightly larger wedge.

the last wedge processed will accumulate the fudge, and might not fall within tolerance. but it should help indicate if your tolerance is too loose, or if you need smaller angular increments to be able to "divvy up" more finely, or any other such "tweaks". an additional run after thoughtful tweaking ought to get you really close.

XanderBakker

It is an interesting script and you gotta love the message at the end: "** SUSAN IS VERY COOL **". However, it is based on the user defining the angles. This can be complex (and time consuming for the trial and error) if you have unevenly distributed points and a central point which is not in the center. The script I posted (although it has its flaws) will determine the angle while evaluating a growth of the polygon by performing a count on the points inside.

JonathanGillespie

This may or may not be what you're looking for, but I had a similar problem a couple of years ago. The solution was a custom script written by someone else. Basically it creates a circular buffer around a central point (or points) split into wedges using user defined angles.

Creating Wedge/Pie Shaped &amp;quot;Buffers&amp;quot; Around Points

As far as I remember it works with the basic license, though I don't recall which extensions are required.

JustinHollenbach1

You could just make a shapefile with equal area wedges and then spatially join or intersect the point file to the newly created shapefile to get points that are within a certain area.

Juanette

P.S. Sheldon, it is great to see you on here. I worked in Big Bend NP for a while and miss the wide open spaces. I would love to have a private conversation and hear more about your work for NPS.

Juanette

LOL Sheldon. I don't think this one time project would justify the expense. But I can dream.

SheldonBkr

Juanette,

Looks like you have some grounds for asking for a GIS upgrade from the County?

Juanette

Oh my...this is all great and has my mind spinning with the various possibilities. I am still deep in the depths of hand placing the last couple of hundred locations that didn't geocode. But I am really looking forward to trying at least a couple of these ideas. I have not used code before in ArcMap but am excited about the possibilities. Unfortunately GIS is only a tiny portion of my job duties (and one that I specifically sought out myself) so I don't get near enough time to work on much beyond the basics. I do really appreciate all this input and frankly am a bit in awe of the great responses. Thank you so much. (And feel free to keep additional ideas coming if you are so inspired.)

Juanette

To answer your questions, Dan.

I do not have Network Analyst. Just basic ArcMap 10.1 with the Spatial Analyst extension.
I can live with the straight line distances and directions. The main goal is to distribute the number of locations to visit. We know that the distances and routes will vary but it is hoped that each inspector will get some locations near the office and some farther. That is hoped to even out the driving burden. Some will have further to drive but others will have to deal with more traffic.
I am looking for 19 territories plus 6 which will only be about half the number of locations.

I do appreciate all your thoughts and insight into this problem.

XanderBakker

... and if you don't have access to the Network Analyst, you could do this in ArcGIS Online, if you have some credits to burn. Plan Routes—ArcGIS Online Help | ArcGIS can help to assign each point to an inspector. This will not create polygons, but will assign each point to a route (or vehicle = inspector).

I believe that a max of 200 points will be assigned per vehicle and each "vehicle/inspector" will burn 1 credit. If there are 1000 points and you have 5 inspectors, 5 routes will be calculated and you will consume 5 credits. So that's not a big thing (no need to take a second mortgage on your house)

DanPatterson_Retired

A circle division would be unduly cruel to just about everyone particularly if the slices of the circle were equal. Since the intent...I hope... is to be fair and minimize clients, drive times and total costs, I am leaning more towards a Network Analyst solution.

In any event, it would be fairly easy and quick to solve if you just wanted to do something like quarter the distribution knowing full well that each quarter would have an unequal number of places to visit and the aspects of drive time and cost would be pretty well thrown out the window.

So back to you again...

do you have the network analyst extension?
could you live with straight line distances and directions as in my previous figure?
how many slices do you need?

Juanette

Here is a quick screen grab. The star is our office and the dots are locations to be inspected.

DanPatterson_Retired

Several possibilities...

If you have an origin point (office) and destination points (the other stuff), you can create points that radiate from the origin to the destination quite easily. BUT, your map may look like this which isn't too helpful but looks really cool in color.

2. You could artificially create a circle to overlay your area and divide into the desired number of sectors needed and sample your points within each sector

3. You could use the network analyst extension (aka the not free extension) and produce a service area AND shortest route to the destinations from the office and divide it up as in step 2. It might look like the above, but there might be fewer lines since the same road could be used to go from the different points (ie from point 59 to 99 to 26 might be the shortest, so you reduce 3 lines to 1, if they were connected by a road.)

4. other ideas pending... a nice screen grab would help fine-tune the above

Juanette

Thanks Chris. This is for inspecting restaurants, pools, hotels etc so I will have point data as soon as I finish cleaning up the geocoding. 🙂

Juanette

I did not know about this add-on. It shows potential. Since this is for inspecting restaurants, hotels, pools etc. I do have a specific set of locations.

ChrisDonohue__GISP

Question - what data is available to use in dividing up the territories? Any chance you have point data showing each inspection?

Also, let me add in who probably has several ideas on how to solve your original proposal:

Dan Patterson

EDIT: Xander Bakker beat me to it. I need to learn how to type faster......

Chris Donohue, GISP

XanderBakker

I haven't tried the tool yet, but Dan Patterson published a tool to calculate Thiessen polygons with a Basic license: http://www.arcgis.com/home/item.html?id=6e9bc6cbf93d4939b2eb04ff8519be47

WesMiller

When i did districts for my codes enforcement inspectors i used the Districting for ArcGIS | Overview the tool is intended for political boundaries but i used five years of historical inspection data to create a balanced set of districts.

ChrisDonohue__GISP

Just wanted to toss out a couple of ideas, though it may be more elaborate than you want:

1. Most of the inspections will likely require transiting a street network. If points could be established at the center of each "territory" (see the idea by Wes Miller , then if you have access to the Network Analyst Extension, you could run a Location Allocation to refine the territories.

ArcGIS Help 10.1 - Network Analyst

2. In terms of figuring out where to place the "center" of each territory, there may possibly be a way to derive those centers using the Geostatsical Analyst Extension. However, I'm not super-familair with this extension, so we'd need someone who is to chime in here.

ArcGIS Help 10.1

Chris Donohue, GISP

Juanette

Unfortunately no, I do not have an advanced license. Just basic ArcMap 10.1 with the Spatial Analyst extension.

WesMiller

Do you have an advanced license? You could put a point at the center of each proposed area then use Create Thiessen Polygons—Help | ArcGIS for Desktop to create the polys.

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