title: Boehm’s Model - Explanation
body: <p>I am reading through &quot;Mythical Man-Month&quot; and near the end in the updates for the 20th anniversary edition it talks a bit about Boehm's model and the optimal time to delivery based upon the exected effort in man-months of a project.</p>
  <p>His statement, when discussing Boehm's model, is:</p>
  <blockquote>
  <p>His results solidly confirm The MM-M’s
  assertion that the trade-off between
  men and months is far from linear,
  that the man-month is indeed mythical
  as a measure of productivity. In
  particular, he finds:[16]</p>
  <p>• There is a
  cost-optimum schedule time to first
  shipment, T = 2.5MM<sup>1/3</sup>. That is,
  the optimum time in months goes as the
  cube root of the expected effort in
  man-months, a figure derived from the
  size estimate and other factors in his
  model. An optimum staffing curve is a
  corollary.</p>
  <p>• The cost curve rises slowly as the planned schedule gets
  longer than the optimum. People with
  more time take more time.</p>
  <p>• The cost
  curve rises sharply as the planned
  schedule gets shorter than the
  optimum.</p>
  <p>• Hardly any projects succeed
  in less than 3/4 of the calculated
  optimum schedule, regardless of the
  number of people applied! This
  quotable result gives the software
  manager solid ammunition when higher
  management is demanding impossible
  schedule commitments</p>
  </blockquote>
  <p>I am having a bit of difficulty in applying this statement practically, I wonder if anyone has any insight as to how this would inform software estimates?  I am particually trying to interpret the estimate formula, as plotted here:
  <a href="http://www.wolframalpha.com/input/?i=graph+T+%3D+2.5+%28x%29%5E1%2F3" rel="nofollow noreferrer">cost-optimum schedule time plot</a></p>
  <p>This seems to indicate that, for a project with 1 man-month of work, there is an cost-optimal time-to-delivery of 2.5 months.  This makes sense, however, if you then assume that there is a project with 5 man-months of work, the plot suggests that the cost-optimal time-to-delivers is 4 months!</p>
  <p>Does this suggest that more man-power should be allocate to deliver within this time frame, or that the estimates are too large?</p>
  <p>Also, how can you estimate optimum staffing levels from this model?
  Thanks</p>