Trying to calculate when our team would be out of SLA, for how long, and what headcount we would need to avoid any days out of SLA. Seems simple at first, but it was not. Tried in excel, but thinking a Python function would be the better way to do this.

Given a stream of WIs coming in per day with their associated KPI in minutes (effort to complete), how many analysts would it take to make sure these WIs all get processed within a 72 hour SLA? What is the mean and max number of analysts needed for the team over the course of the year based on the daily WIs coming in?

Assumptions:

• Asymmetrical workload coming in for each day, with peaks and valleys of work. Assume a few large days in a row of between 10k – 20k minutes of work coming in several times a year, with most days below 2000 minutes of WIs.
• An analyst can process 420 minutes of WIs per day. Assume there are 20 analysts on the team.
• KPI is 30 min per WI

Tried formulas in excel for calculating trailing 3 day (72 hour) backlog of WIs, and when they would be processed in the preceding days, but cant come up with an appropriate excel formula that tells me the needed info. Happy to use a python script to run this on a file. Appreciate the help!