We always have to make simplifying assumptions when modelling the real world. Here are ours:
- All the new hires all come on board on the first day of the increased staffing.
- The mix of new hires is the same as the mix of the existing team.
- The new hires ramp up continuously during the remainder of the project. The ramp-up profile will be the usual S-curve, but its exact shape is unknown. We choose to characterize the integral under the S-curve by one average value, P, for the entire interval.
- By the end of the project, the new hire average productivity achieves the same value as that of the existing team.
- The value for D, the drag, is an average over the whole organization for the entire period.
- The average wage rate for the new hires is the same as that of the existing team; this follows from #2.
- After ramp-up, the organization does not lose per-capita productivity just because it has become larger. This follows from #4.
It is worth noting that the designer of a nomograph has the job of laying it out in a way that makes it very easy to use. The directions for its use must be indicated right on the nomograph itself. The scales must also be labeled so unambiguously that getting the input wrong is virtually impossible.
Also, as the scales typically encompass only the regions of interest of the key variables, it is usually clear when one is trying to do something "off the chart". Needless to say, the scales always have the correct system of units indicated, so that errors of this type are minimized.
Nomographs have the interesting property of solving equations both explicitly and implicitly. You can find any missing variable or combination of variables by "working backwards." That is, instead of proceeding with the first two variables and going left to right across the page, one can start with "the answer" and work backwards to see what combination of input variables can get you to that result.
Another virtue is the ability to do sensitivity analysis quickly by experimenting with different combinations of variables, holding some fixed and seeing the leeway you have with the remaining ones. All in all, it is a valuable tool for investigating the type of problem described.