According to world-famous efficiency expert Dr. I. E. Pertchart, the productivity P of a group of N engineers working on the same project is given by his productivity formula

P=(1+x_1)*(1+x_2)*...*(1+x_k).

Here the project has been split into k <= N independent subprojects with x_i of the engineers assigned to the i-th subproject, x_1+x_2+...+x_k=N. Over all possible splits of the engineers, what are the maximum and minimum values of P that can be achieved? Proof?

The minimum value of P is N+1, where there is only one subproject with everyone working on it, and the maximum is 2^n, where everyone works on there own independent subproject.

To see this, note that every time I take one person away from an independent project to work with someone else, I replace two factors of 2 with one factor of 3.

This can be formalized by induction on N. For N=2, max is 4 and min is 3. If the best way to use N-1 engineers is with N-1 subprojects, then the best way to add one more is with one more subproject.

There is probably a more direct way to prove this.

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Note: I realize the problem is fictitious, but as an engineering manager, I can say that this formula is not correct in real life (except perhaps in unusual situations). For example, programming in pairs has been shown to be a more productive way to get complex software projects done correctly.

Edited on February 9, 2005, 2:48 pm

Posted by SteveH on 2005-02-09 14:43:17