According to PUTNAM, the project effort is inversely proportional to the…
2018
According to PUTNAM, the project effort is inversely proportional to the fourth power of the development time. Doubling the development schedule for a 100 Person-Month (PM) project would reduce the project effort to
- A.
50 PM
- B.
7.16 PM
- C.
25 PM
- D.
6.25 PM
Attempted by 4 students.
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Correct answer: D
Putnam's software equation (derived from the Rayleigh-Norden staffing model) states that, for a project of fixed size and complexity, effort (E) is inversely proportional to the fourth power of development time (T): E is proportional to 1/T4. A small change in schedule therefore produces a very large change in effort -- stretching the schedule sharply cuts effort, while compressing it sharply raises effort.
Let the original development time be T, giving an original effort of E1 = 100 PM.
Doubling the schedule makes the new development time 2T.
Since E is proportional to 1/T4, the ratio of efforts is E2/E1 = (T / 2T)4 = (1/2)4 = 1/16.
So E2 = E1 divided by 16 = 100 divided by 16 = 6.25 PM.
Cross-check: 6.25 PM multiplied by 16 gives exactly 100 PM, recovering the original effort and confirming the calculation. This fourth-power sensitivity is precisely why Putnam's model treats schedule compression as extremely costly -- cutting the schedule even slightly drives effort up sharply, while a modest schedule extension yields disproportionately large effort savings.