Musings on project management: Do the math!

Monday, January 20, 2014

Do the math!

Heard about "merge bias"?

Actually, some of us have. And, probably to everyone's relief it's not one more in a long list of cognitive biases.

So, here's the problem: You have two or more predecessor activities (see also: gates, tasks, swim lanes, projects) joining independently to form a finish-to-start dependency on a successor activity. If the predecessors are both/all supposed to finish (or get DONE) at the set time to set off the successor activity, should you worry?

Yes, you should. Where the activities merge, like at a gate, there is a bias toward having to shift the schedule to the right (see: schedule slip) in order to maintain confidence in the schedule end date.

In other words, by example for two paths, if there is a 50-50 chance of both paths finishing independently together, then there is only 1 chance in 4 that the successor will start on time:

Activity	1.On time	1.Late
2.On time	On time	Late
2.Late	Late	Late

Saying it with confidence: The graphic gets your attention, but it's really limited for understanding what's going on. It's a matter of 'confidence'. In the case illustrated, the proper way to understand this is:

"Your confidence that the successor can start 'on time or earlier' is 25% or less. Your confidence that the successor task will start late is 75%, or more"

How much earlier? How much later? You don't know from what I've said so far, but you can get a handle on it with a Monte Carlo simulation.

Do the math: If I replace the labels "on time" and "late" with quantitative probabilities, you can see that the probability in each cell is the product of the row-column intersection. To wit: 0.5 * 0.5 = 0.25

So, your challenge as schedule architect is to increase the confidence of the successor F-S. How to do it? Here's an idea: re-architect the schedule from 2 paths to 3 simpler paths, each with higher probabilities on account of their simplicity.

Now the graphics for three paths of different probabilities gets too awkward because now you need a figure of 8 (2^3) intersections rather than a figure of 4 (2^2) intersections. Best that you stick with the quantitative probabilities.

You might get something like this, as an example, of three independent activities (probability shown as on-time, so p[late] = 1 - p[on-time]):

Activity 1: 70%
Activity 2: 65%
Activity 3: 75%

The joint probability of on-time is their product: 34%, slightly better than the 25% figure of the two lower probability higher complexity paths.

Now, of course, this re-architecture can go the wrong way: the improvement in probability has to be fairly large to overcome the three path merge bias. Nonetheless, this option is available for risk managers and schedule architects.