Monday, 21 September 2015

The little law of project management

OK, so you think project management is an overhead. You know what has to be done, so why not just get on with it? All this paperwork just adds time (and cost)!

If I could have a penny for every time I’ve heard this or seen it written I’d be as rich as the proverbial millionaire! (Well a bit of an overstatement, but you get my meaning).
Well, for anyone who is a PM sceptic (and maybe even those who aren’t) let me introduce you to Little’s Law.

Little’s Law

Dr. John D.C. Little, Institute Professor at the Massachusetts Institute of Technology, developed a queuing theory law known as Little’s Law, in 1961. This states:
"The average number of customers in a system (over some interval) is equal to their average arrival rate, multiplied by their average time in the system."
Or, more formally:
“the average number of items in a queuing system, denoted L, equals the average arrival rate of items to the system, λ, multiplied by the average waiting time of an item in the system, W . Thus, L=λW.” [1]

What on earth has this got to do with project management?

Well, a lot, actually. Little’s Law can be applied to any situation, not just queuing, where work of some kind has to be done because the three variables in the Law are present in all types of work:

  • L is also known as Work in Progress (WiP)
  • λ is also known as Throughput (T)
  • W is also called Cycle Time (CT, or sometimes Lead Time)

All three of these pertain to projects as this very simple example shows.

Let us assume that on average a team is delivering 5 projects at any one time. WiP = 5. Let us also assume that Throughput is, on average, 2 projects per month completed. Using Little’s Law, we can change the formula to calculate cycle time – i.e. W = L/ λ or (dispensing with the Greek) CT = WiP/T.

This gives us 5/2 = 2.5 months (per project).

Let’s now say that the boss says we need to take on two new projects this month, in addition to those we’re already doing. No need for project planning, etc. … “Just do it”. Well this will actually impact all other projects as well as the two new ones, because Little’s Law tells that that WiP has now increased from 5 to 7 so cycle time now is 7/2 = 3.5 months.

This seems a bit counter-intuitive, but Little’s Law has been shown to hold time and time again. The above figures are, of course, averages – but if the average time it takes to complete projects increases this means that although some may still get finished on time or earlier, on average most will take longer than before.

Information Technology (IT) departments are often under pressure to take on additional projects for their customers, thus increasing WIP. This immediately causes the project completion time (CT) for all projects to increase and may explain why so many IT projects take longer than expected. This is worth repeating: new projects added to the list of projects immediately causes the time it takes to complete each individual project to increase!

What you get is a slowdown in the delivery of all projects because resources get too thinly spread or you get bottlenecks emerging where a scarce resource is present (e.g. the one or two expert database administrators). So you start to fail to meet delivery times (even with projects already underway), have poorer performance, and a resultant reputation that projects are never finished (on time). All because you tried to do the “right thing” by responding to customer demand and taking on more projects.

That’s just one reason why project management is so important, because planning forces you to take account of the resources you have and to schedule the project accordingly.


[1] Little, J.D.C.(2011) ‘Little’s Law as Viewed on Its 50th Anniversary’ Operations Research Vol. 59, No. 3, May–June 2011, pp. 536–549, available online at:  (accessed 21 Sept 2-15)

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