f(x) = y
where
x is the data frame with variables Provider, Start_month, Start_qr and client_volume
y is the
over some forecast horizon.
f is the function or composite function to convert x to y
The first requirement for f is to calculate the duration of each completed program (A,B,C\dots) from the variables contained in x.
x is clearly insufficient to make that calculation because the only date information provided is a variable with an open ended range—there is a start date but no end date.
The purpose of a reprex. See the FAQ is to provide information sufficient to reflect the problem. The data doesn't have to be all the data at hand, all of the variables, or even the same data. Representative data from a built-in data set is fine or even synthetic data. But it must be complete to the extent needed to set up the problem. Here it is not.