Way back in 1975 Frederick Brooks wrote a famous book, The Mythical Man-Month, stating: "Adding manpower to a late software project makes it later."
Other than the now-all-too-obvious sexist nature of his words ("manpower", "Man-Month"), Brooks Law has stood the test of time. Three graphs from the original book with their original captions are reproduced in the figure [the yellow, non-sexist annotation is mine].
The first caption suggests and then dismisses the idea that "If one man takes 10 months to do a job, 10 men can do it in one month" saying "This may be true of picking cotton." (OOPS, is the mention of picking cotton racist? Perhaps he should have used the more familiar "nine women could produce a baby in one month" but that would be sexist again. OY! :^)
He then notes that "even on tasks that can be nicely partitioned among people, the additional communication required adds to the total work, increasing the schedule." That is the well known Law of Diminishing Returns, which does have a mathematical formula. But, as his second graph indicates, more people will still speed the job.
Finally, he says of his last figure (called the "Bathtub" curve) , "Since software construction is complex, the communications overhead is great. Adding more men can lengthen, rather than shorten, the schedule." That seems like verbal flailing of his arms - but, nevertheless IT IS TRUE! And it applies not only to software engineering, but to any complex engineering or business or political or legal or medical task that requires significant interaction between professionals. But, look at Brooks graphs - there are no numbers on the axes! How can a Law be unquantified?
Since my PhD is in Hierarchy Theory, I have considered this a personal challenge and have written a couple of [former] Google Knols about Management Span of Control Advisor and Quantifying Brooks Mythical Man-Month, between them garnering over 6,000 page views! A few months ago I received an email from a very smart Knol reader who was utilizing my work in planning the management structure for a project at his company and he wanted an Excel spreadsheet to help with the task. I sent him an old spreadsheet I had used to make some graphs for my Knol and he used it (giving me credit in the PowerPoint charts he asked me to review and that he presented to his management).
But, my old spreadsheet -while useful to this one very capable and perceptive person- was not easy to use nor did it apply to multi-level hierarchies. I knew I could do better! That triggered me to create a Management Span of Control Advisor that would put my theory into a form so simple that even a manager could use it (:^).
The happy result is my just-published [Former] Google Knol Management Span of Control Advisor and a comprehensive yet easy to use spreadsheet to go along with it.
The illustration from my new spreadsheet shows how Brooks Law applies mainly to a One Level department (BLUE bathtub curve), but it can be "drained" with a multilevel hierarchy (Two Level structure - PINK curve and a Three Level structure - GREEN curve).
Please feel free to have a look at my new Knol and download and try out the companion Excel spreadsheet. As always, comments are appreciated!
PS: My students at the University of Maryland University College will be using this new Knol and spreadsheet in the online grad course in System Engineering I teach there and which starts in a couple weeks. Most of them are professionals in the Information Technology (IT) industry (or related military work) and many are going for their Masters Degree to help them become better IT managers or move from technical work to IT management.