Did you know that missed deadlines have a reason that can be explained with math? Maybe you know the TV series Numb3rs. Charly Eppes helps his brother Don of the FBI to investigate cases. Charly is math professor and he always has a nice mathematical explanation for what is happening and how to solve the case. (By the way – that is an excellent example of two knowledge workers!) Today I want to explain to you mathematically, why deadlines in knowledge work are missed again and again. I know – it does not happen to you. But just in case you are curious.
Maybe you think that working harder would solve the problem. But all the time you are struggling against a mathematical law.
Say we have a case that has to be broken down into workitems. These workitems have dependencies. Some have, some have not. So it is a network of workitems, or mathematically spoken a directed acyclic graph. You can think about it like a BPMN process without loops. Another mathematical term is lattice. Now we can estimate the duration of each workitem and by using standard project planning techniques we can calculate the planned end time of the project, buffer times of the workitems and the critical path – i.e. the workitems that have a buffer time of zero. You surely have heard of it.
When I was in the seminary learning the technique I said to the teacher: I have doubts about this technique. It is well known that most projects don’t follow this plan, but are late. So there must be something wrong with it. Why not plan more buffer time from the beginning? The teacher said I am not in the position to question such a technique, but I have to learn it. So far so bad.
Later I was in a seminary about statistical project planning. Very interesting. Each workitem did have a probability distribution instead of only a planned duration. Of course the probability distribution has an expectancy value and a variance. One tends to think the expectancy value of the workitems duration probability distribution should be equal to the planned duration in deterministic (i.e. non probabilistic) project planning. And one tends to think, that the expectancy value of the duration of the whole project is the sum of all expectancy values of the duration of workitems that are on the “critical path” of the project. But that is not true. Something unexpected happens here – mathematically.
If you use the means of statistics to calculate the probability distribution of the duration of the whole project it turns out, that the expectancy value of the project duration is always bigger or equal than the sum of the expectancy values of the workitems on the “critical path”. THAT is strange. Even if all workitems behave according to their probability distribution – i.e. some take longer but others are completed faster – even then the whole project takes longer.
I am not talking about bad estimations here. I am not talking about the problems that appear, if all workitems take longer than planned or additional workitems are needed. I talk about perfect guesses and a perfectly planned process. EVEN THEN – the whole project takes longer.
Why is this so?
The answer is this: There are dependencies between the workitems. Because of these dependencies certain workitems can’t be started, until others are completed. If one workitem in the chain is delayed, it delays the start of other workitems as well. But if one is faster than planned, it does not necessarily speed up other workitems. Simply said: delays add up while completing ahead of time don’t.
It is the same reason why there is a traffic jam on a highway simply because there are many cars. Why don’t they all drive 120 kilometers per hour? Just because the breaking adds up between the cars and accelerating the car does not.
Of course the effect is much stronger, if the variance of the probability distribution for the tasks is bigger – which is the case with knowledge work.
So – I got my satisfaction. The first teacher was wrong, I was right. I can prove it mathematically 
.
And you have a good excuse for the next time you miss a deadline. You can say you worked very hard, but there is a mathematical law ….