Xander Bakker, nice work addressing the GIS portion of the problem. Once the GIS portion is addressed, then comes the operations research or optimization portion of the question, i.e., what is the true maximum parcels and what configuration represents that true maximum.
I did some futzing over the weekend. Since the OP didn't upload any sample data, I decided to use Esri's backyard: City of Redlands Open Data: Open Data Zoning. To simplify the problem, and to not get into the issue of property records directly, I decided to use Zoning units in the central part of Redlands around Esri's campus.
I made the following assumptions:
- Parcels/geometries for consideration are Single-Family Residential (sample size - 71)
- Activity cannot be allowed within 500 ft. of parcel that already allows activity (buffer distance)
- No restrictions between adjacent Single-Family Residential and other zoning categories (edge condition)
I didn't have time to apply a true optimization model, so I thought it would be interesting to look at some basic simulations. The general approach:
- Randomly select first parcel
- Add parcel OID to selection list
- Create spatial selection polygon
- Randomly select next parcel
- Buffer selected parcel 500 ft.
- if parcel is disjoint with spatial selection polygon:
- Add parcel OID to selection list
- Union parcel with spatial selection polygon
- Repeat step 2 until sample size exhausted.
- Repeat steps 1 through 3 for x number of simulations
There are likely ways to optimize the compute time of the approach above, but I didn't bother to spend the time since my approach could simulate 1,000 scenarios in a few minutes.
Since 1,000 scenarios ran fairly quick, I just did that and 10,000 scenarios. For the 1,000 scenario runs I did, I always ended up with 1,000 unique outcomes. For the 10,000 scenario runs I did, I would typically end up with 9,980 or so unique outcomes.
Looking at one of the 10,000 scenario runs, the outcomes breakdown to:
Number Parcels in Solution/Outcome | Prevalence |
---|
10 | 20 |
11 | 100 |
12 | 442 |
13 | 1164 |
14 | 2104 |
15 | 2533 |
16 | 2139 |
17 | 1098 |
18 | 335 |
19 | 43 |
Looking at the distribution of solutions is interesting in its own right. It appears the minimum number of parcels that meet the conditions is likely 10. There might be a 9 solution out there somewhere, but would decisions based on this information change much whether the minimum is 9 or 10? On the opposite end, the maximum number of parcels that meet the condition is likely 19. Similar to the minimum, there may be a 20 or 21 solution that exists, but does knowing the true maximum gain much.
Assuming for the sake of discussion that 19 is the maximum number of parcels that meet the conditions, 43 different combinations were found that provide 19 parcels. Looking just at the prevalence of individual parcels in those 43 combinations:
Looking at the graphic, you can see there are 4 parcels that are in all of the 43 combinations, and 3 of those 4 are adjacent to other zoning categories. Since there is no penalty for being adjacent to other zoning categories, it makes sense that the higher prevalence parcels are scattered around the boundaries of the block of single-family residential parcels.
Getting back to my original comment to the OP, this is much more than just a GIS question. Since allowed activities will likely be approved on a first-come-first-approved basis, each time an activity is approved for a given parcel, it influences how many total parcels might be selected in the end. Looking back at the table of results, there are 20 outcomes that would only allow for 10 parcels to be selected.