All,

I'm not a math guy so I'm reaching out for help.  I need to create an equation (or formula, or function, not sure which)  to address my organizations personnel shortfalls and the way to get it back on track.

We have an authorized staffing strength.  Let's call this A.  This is the goal we are trying to achieve.

We have our actual number of people on hand.  These are the people that show up to work. Let's call this B.

We have an annual attrition rate.  C.

There is some delta we are trying to close:  Getting from B to A, accounting for annual attrition (C).  Let's call this D

There are three major sub-organizations in the larger organization.  Each needs to get from A to B in a set amount of time (T) .  Group 1 has 4 years.  Group 2 has 4.5 years and Group 3 has 6 years.

How would I write this out mathematically to account for the goal, on-hand, annual attrition and time?

Again, not a math guy so I don't want to write this out incorrectly for a presentation.

Thanks.

I wonder if this is a job for an AI?

Curiously enough, I cleaned up the text a bit and put into ChatGPT.  Below is what it spit out.  Wonder if it is competent(I am also not a math guy)

OUTPUT:
One possible equation to represent the personnel shortfall and the time needed to achieve the authorized staffing strength (A) for each sub-organization could be:

For Group 1:
D1 = A - B1 + (C * T1)

For Group 2:
D2 = A - B2 + (C * T2)

For Group 3:
D3 = A - B3 + (C * T3)

where:

D1, D2, and D3 represent the delta or the personnel shortfall for each sub-organization.
B1, B2, and B3 represent the actual number of people on hand for each sub-organization.
T1, T2, and T3 represent the time in years that each sub-organization has to reach the authorized staffing strength.
C represents the annual attrition rate, which is assumed to be constant over time.
The equation assumes that the personnel shortfall (D) can be closed by hiring new employees and that attrition occurs uniformly over time.
To solve for the required rate of hiring or the number of hires needed to reach the authorized staffing strength within the specified time frame, you can rearrange the equation to solve for the unknown variable:

For Group 1:
h1 = D1 / (C * T1)

For Group 2:
h2 = D2 / (C * T2)

For Group 3:
h3 = D3 / (C * T3)

where:

h1, h2, and h3 represent the required rate of hiring (in terms of number of hires per year) for each sub-organization to reach the authorized staffing strength within the specified time frame.

Meth experts,  I need help creating and explosion???

Over the interval T (years), you want your new staffing level (A, people) to be equal to your growth rate (D, people/year) times T plus your current staffing level (B, people), minus your attrition rate (C, people/year) times your interval T.

A = D*T + B - C*T


Solving for the needed growth rate,

-> D = (A-B+C*T)/T