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As a starting point the Tableau public dashboard you have referenced is pre calculated. The 'distance' filter only has pre-calculated values for yes and no and only allows 0.25 to 1 in the distances at 0.25 steps as these are the values that have been pre calculated.
As for your dataset it sounds like an inefficient task to pre-calculated distances for all iterations (100,0002 = 1,000,000,000 or 1 billion combinations)
Assuming that you have decimal latitude and longitude figures the distance between two points can be calculated as:
ACOS(COS(RADIANS(90-[Latitude1])) *COS(RADIANS(90-[Latitude2])) +SIN(RADIANS(90-[Latitude1])) *SIN(RADIANS(90-[Latitude2])) *COS(RADIANS([Longitude 1]-[Longitude 2]))) *6371
The above formula will work in tableau although as stated the 1 billion combinations is too many to be feasible.
Instead, to replicate the dashboard that you looked at, I would look to pre-calculate the minimum distance to the nearest site, outside of tableau i.e. each of the 100,000 data items may look like:
Store name, Latitude, Longitude, Distance to nearest store, any other data items...
I've attached an example of this in tableau with a map. Please note the map looks awful as I've randomly generated worldwide co-ordinates completely at random for 1000 data items.
As for calculating the initial data set. This 'could' be done in Excel as a one off although for 100,000 data items this would take some time. I've attached an excel spread sheet with a Macro showing one way to achieve this. Hopefully you are familiar with VBA although this macro has been quickly written and is reliant on cell references but hopefully you get the idea.
Finally, the 'circles' around the stores are created in the example using pre-calculated paths. In the example you've linked to you will actually see these are 16 sided polygons. I have not implemented this in my example as this would multiply the data set by 16 times. For completeness the data in the starbucks example is for 9,714 stores but actually contains 887,523 lines of data to facilitate distances and the circles. The example I've given without circles only requires one line per store.
I hope this points you in the right direction. That said this is only one possibility, there are many tableau experts on here who may have a better solution.
Tableau Public is blocked here at work, but if you go there and search my name, you will find a dashboard created for the BMV that has the pieces that you need in order to do this.