How do I calculate working business minutes?
If your reports are based on a data warehouse that is dimensionally modelled (generally the case for business intelligence solutions), it is highly probable there is a date dimension and time dimension.

If there are no such objects, it may be very useful to create them as they become highly re-usable as other reports are required.

In the date dimension, there should be an IsHolidayFlag column. In the time dimension, there should be an IsBusinessMinuteFlag column (depending on the grain of this dimension, it may be IsBusinessSecondFlag).

The query would then be relatively straight forward and quick, provided the indexes are correct. There is an overhead with the CROSS JOIN (which could be created as a view for re-usability), but for 200,000 rows, it should be negligible.

SELECT  i.IncidentID,
       'WorkMinutesInRange' = SUM(CASE WHEN d.IsHolidayFlag = 'N' AND t.IsBusinessMinuteFlag = 'Y' THEN 1 ELSE 0 END)
FROM    dbo.Incidents i
        INNER JOIN Dim_Date d
            ON d.CalendarDate BETWEEN i.CreatedOn AND i.ResolvedOn
        CROSS JOIN Dim_Time t
GROUP BY i.IncidentID