Approaches to A/B testing when you can't randomize on the user level
I would recommend against switch back as the purchase data is likely to exhibit seasonality (e.g. 2pm - 6pm / tuesdays exhibit lower volume, December exhibit higher volumes, company running advertisements during certain months etc.), which would become an unnecessary exogenous factor that complicates the post implementation analysis.

I am inclined towards the causal impact approach. However, there are certain things that should be checked before selecting the stores as control vs. test (it is a kick-start list, please feel free to adapt to your business domain).


Decide on the KPI to be measured as the objective, is that revenue per customer? Profit per customer? Or total profit per store? Is the algorithm designed to increase per customer KPI or more customers?
Check that the stores selected have some history to give assurance that they were similar in terms of the selected KPI before the implementation of the tests. Remember to remove outlier customers / transactions.
Check that enough stores are selected in control vs. test buckets to detect a desired threshold increase that is statistically significant.


Hope this helps! :)