Little’s Law and Kanban

Little’s Law is an important concept for Kanban.  It has its roots in manufacturing and operations management as a technique for characterizing the utilization and capacity of a system to produce finished work.

Components of the equation

Work in Progress (WIP) = The average number of items in a system (over some interval)

Throughput (TH) = is the rate at which work travels through the system in a given unit of time

Cycle Time (CT) = Length of time a work item is in the system.

Definition

The basic equation defines that the number of items in the system (WIP) can be calculated as the throughput of the system (TH) multiplied by how long it takes to complete the work (CT)

Symbolically, this can be represented as:

WIP = TH * CT

The other useful variations of this equation are:

TH = WIP/CT

CT = WIP/TH

Examples

Here are a few examples of applying Little’s Law.  Note that if you know any two of the variables, you can always calculate the third.  In practice, I tend to use the variant TH = WIP/CT most often since I am usually trying to determine the throughput of a team or group of teams.  Work in Progress and Cycle Time are usually known or, in the case of WIP, it can be set as a constraint.

Example 1

A checkout system has 4 lanes open.  On average, each customer takes 7 minutes to checkout.  What is the throughput of the system?

Work in Progress (WIP) = 4 lanes

Cycle time (CT) = 7 minutes

Throughput (TH) = 4/7 minutes

Throughput = .57 customers per minute

Important concept – throughput is always per unit of time, in this case per minute!  It is critical that the throughput time units and cycle time units be identical.

Example 2

A development team can support 3 backlog items simultaneously.  On average, each backlog item takes 8 business  days to complete.  How many backlog items can be completed in a 12 week release?

Work in Progress (WIP) = 3 backlog items

Cycle time (CT) = 8 days

Throughput (TH) = .375 items per day (3 divided by 8)

Next, we need to convert the release length to days so that the units of time are consistent

Release Duration = 60 Days  = (12 weeks * 5 work days/week)

Estimated backlog items completed = (TH  * Release Duration) or (.375 * 60)

22.5 items will be completed during the release

Example 3

A variation of example 2 is that the backlog size is known, and you must forecast how long it will take to complete the backlog.  The same development team can support 3 backlog items simultaneously.  On average, each backlog item takes 8 business days to complete.  Given a backlog of 40 items, how long will it take to complete the backlog?

Work in Progress (WIP) = 3 backlog items

Cycle time (CT) = 8 days

Throughput (TH) = .375 items per day (3 divided by 8)

The number of days to complete the backlog is simply the number ofbacklog items divided by throughput:

40 / .375 =106.6 days

Cycle time nuances when forecasting

In the examples above, I referenced an “average” cycle time.  In practice, there is a great deal of variability in cycle time.  The straight line estimating done above is a reasonable approximation, but more advanced forecasting tools, such as Kanbansim from Focused Objectives, look at the distribution of cycle times and simulate the outcome using the distribution of values.

Let’s look at a set of actual cycle times for a team (in days): 4, 5, 10, 14, 14, 14, 17.

The average is 11.14, but the median is 14.  Also, 14 is the most frequently occurring value.  An advanced foresting tool will use a Monte Carlo simulation to select values from the actual cycle times, rather than use an average value.

Cycle Time and Waste

The challenge of a good Lean practitioner is to understand what component of the cycle time is waste due to blockage or inefficiency.  The diagram below shows how waste is interspersed with productive work.  It is not usually a big chunk of time that can be easily removed.

 

Cycle time

Summary

Little’s Law is an important tool for the Lean practitioner utilizing Kanban.  There is a large volume of information available on this subject if you would like to read further.

 

 

 

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