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I am attempting to confirm some calculations given to me during class, regarding the work duration of different projects.

This table concerns a 100 man-month project, where using the Optimal Span Hypothesis the the efficiency percentage is calculated. See below for table of results.

Table of results

I am able to replicate the results in the efficiency column using the following Matlab code.

 hold on
 for N = 5:500
   ESQRT = 100*sqrt(N - 1)/(N)
   EOSH = -100*((N - 1)/N)*(2/(N - 2))*log2(2/(N - 2))/0.53

   EC = ESQRT*EOSH*(N/(N-1))/100

   plot(N,EC,'*')
 end

Where at N = 6 i get 35.1% and N = 9 i get 30.6% etc.

Using a given formula of $$W = N^{0.5} $$ where W is work and N numbers of agents. The work is then converted into monthly duration by the following $$months = \frac{manmonths}{W}$$where months is the calculated duration in months and manmonths is the project duration.

If there is one agent, at 100% efficiency i can replicate the duration of 8.3 years. $$W = 1^{0.5} = 1, months = \frac{100}{1}, years = \frac{100}{12} = 8.333$$

My Problem is then: I can't recreate the duration for the 6 agent and 9 agent projects. I have tried changing the work formula to incooperate the efficiency, but it yields incorrect results (With the 6 agents case it yields 5.7 years.) $$work = (ef\% \cdot N)^{0.5}$$

I'm almost certain the the solution is fairly obvious and I'm just missing something. Thank you in advance.

1 Answers 1

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It seems like the duration column is computed as $8.3 / (N \cdot \textrm{ef%})$, and that $W = N^{0.5}$ is not used. The cost column is computed as the (unrounded) duration column multiplied with $N$ (which simplifies to $8.3/\textrm{ef%}$).