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Case Assignment based on number of cases assigned per person per day

I'm currently using a "round robin" case assignment method that uses the (Case Number)MOD(Number of Engineers) to determine how to assign the cases.  However, this has multiple flaws - expecially when multiple cases get assigned to one person due to them being for the same customer, then other engineers get "skipped", etc.
I want to assign cases base on how many have been assigned for that day.  For example, each engineer will have a "counter" that tracks how many cases were assigned to them that day.  Each case would get assigned to the next engineer in line that has the fewest number of cases assigned to them that day.  If there is a "tie" - meaning all engineers have been assigned the same number of cases that day, then it should default to a secondary rule which just numbers the engineers 1, 2, 3 etch.
anyone have ideas on how to accomplish this?  I just want to assign the cases equally per day accross my engineers.
Chris ShadeChris Shade
Hi BluIdTi2gr,

I know an option but it would require some custom fields on the user object and the use of process builder and flows.  If that is within your skill set let me know and I'll walk you through it.