I’m currently reading the advanced ScrumBan book Scrumban [R]Evolution – Getting the most out of Agile, Scrum and Lean, Kanban by Ajay Reddy and found a nice extension of Little’s Law that I would like to share with this post.

#### A short recap on Little’s Law

Formula 1

$\mathrm{average output \left(per time period\right)}=\frac{\mathrm{average inventory of work \left(per time period\right)}}{\mathrm{average lead time of work \left(per time period\right)}}$

The average inventory of work is the average number of user stories between the starting and end points for a given period of time (WIP).

The average lead time is the average amount of time it takes for a work item to move from the first stage of a production process to the end of that process.

#### And the extension for release planning with Little’s Law

Based on Project Planning Using Little’s Law by dimitar.bakardzhiev the formula can be extend to:

Formula 2

$\mathrm{Average WIP}\phantom{\rule{0.2em}{0ex}}\text{(The amount of developers,resources,… needed)}\phantom{\rule{0.2em}{0ex}}=\phantom{\rule{0.2em}{0ex}}\phantom{\rule{0ex}{0ex}}\mathrm{Average Lead Time}\phantom{\rule{0.2em}{0ex}}\left(\frac{\mathrm{number of user stories}}{\mathrm{Total project time}}\right)$
Formula 3

$\mathrm{\left(Project/Release\right) lead time}\phantom{\rule{0.2em}{0ex}}=\phantom{\rule{0.2em}{0ex}}\left(\frac{\mathrm{number of user stories}}{\mathrm{Average Throughput}}\right)$

test

Let’s consider the following example… Given:

• each team member averaging 2 items of work in progress at any point in time
• a teams average completion rate of 28 user stories per 2 weeks iteration (14 stories per week)
• an average lead time of 0.9 weeks per user story
• the release backlog with 675 user stories
and we search for the optimal staffing to complete the project within 26 weeks – by applying Formula 2:

$\mathrm{Average WIP}\phantom{\rule{0.2em}{0ex}}\phantom{\rule{0.2em}{0ex}}=\phantom{\rule{0.2em}{0ex}}0.9\phantom{\rule{0.2em}{0ex}}\left(\frac{675}{26}\right)\phantom{\rule{0.2em}{0ex}}=\phantom{\rule{0.2em}{0ex}}23.36$

This means you’ll need 24/2 (average WIP of every team member) = 12 team members to accomplish the project within 26 weeks.

And what happens if you have to finish it in 18 weeks?

$\mathrm{Average WIP}\phantom{\rule{0.2em}{0ex}}\phantom{\rule{0.2em}{0ex}}=\phantom{\rule{0.2em}{0ex}}0.9\phantom{\rule{0.2em}{0ex}}\left(\frac{675}{18}\right)\phantom{\rule{0.2em}{0ex}}=\phantom{\rule{0.2em}{0ex}}33.75$

This means you’ll need 34/2 = 17 team members to accomplish the project within 18 weeks.

Now let’s fix the number of people to 12 (2 teams with 6 team members each) and we need to forecast the project duration.

$\mathrm{Duration}\phantom{\rule{0.2em}{0ex}}\phantom{\rule{0.2em}{0ex}}=\phantom{\rule{0.2em}{0ex}}\mathrm{number of stories}\phantom{\rule{0.2em}{0ex}}\left(\frac{\mathrm{average lead time}}{\mathrm{average WIP}}\right)$

$\mathrm{Duration}\phantom{\rule{0.2em}{0ex}}\phantom{\rule{0.2em}{0ex}}=\phantom{\rule{0.2em}{0ex}}675\phantom{\rule{0.2em}{0ex}}\left(\frac{0.9}{24}\right)\phantom{\rule{0.2em}{0ex}}=\phantom{\rule{0.2em}{0ex}}25.3\mathrm{weeks}$

What a nice extension for release planning.

In addition we need to consider that work delivery rates in projects are not uniform but tend to follow a fairly predictable S-Curve (with delays in the beginning and at the end of a project).

Little’s Law can therefore be applied with high confidence to only the middle portion of most projects (approximately 60% of total project duration).

For the remaining 40% of the project we need to work with a project buffer that can be calculated using the formula I’ll describe in my next post (just subscribe to receive your weekly updates right in your inbox ;-).