In this blog entry, we explore the intriguing world of Little’s Law, lead time, cycle time, and throughput, using a unique whisky analogy. Sit back, pour yourself a glass of your favorite Scotch (perhaps a Macallan 12), and let’s dive into the intricacies of these concepts.
The Whisky Analogy: Setting the Stage
While sitting at my dining table I was thinking about a way to explain Little Law, lead tine, cycle time and throughput. This idea came to mind once I did pour myself a glass of whisky. It was the last dose of a Macallan 12 bottle. I removed the empty bottle from the bar, and took a note to buy another one.
Problem Statements A and B for exemplifying Little Law
Let’s begin with two problem statements, both similar was to look at the same situation.
Problem Statement A: At home, I have 12 bottles of whisky at my bar. I consume and purchase an average of 6 whisky bottles per year. What is the average time each whisky bottle stays in my bar?
Or, stating the same problem in a different way:
Problem Statement B: At home, I have 12 bottles of whisky at my bar. In average, I finish (and purchase) one whisky bottle every two months. What is the average time each whisky bottle stays in my bar?
From the problem statements I can get the following parameters:
The inventory or WIP is 12 bottles. (Problem statement A and B)
Throughput is 6 bottles per 12 months (Problem statement A)
Average Cycle time is 2 months per bottle(Problem statement B)
And the question is the average lead time
I will solve the problem two ways:
Solutions Unveiled: Two Paths to the Same Answer
Solution 1:
WIP = Throughput x Average Lead Time
12 bottles = 6 bottles /12 months x Average Lead Time,
Therefore, Average Lead Time = 24 months
Solution 2:
Average Lead Time = WIP x Average Cycle Time
Average Lead Time = 12 bottles x 2 months/bottle
Therefore, Average Lead Time = 24 months
“The average number of work items in a stable system is equal to their average completion rate, multiplied by their average time in the system.” ~ John Little, 1961
“The average number of work items in a stable system is equal to their average completion rate, multiplied by their average time in the system.” This profound wisdom, articulated by John Little in 1961, forms the essence of Little’s Law, a fundamental theorem in queuing theory. The text above, sourced from “A Proof for the Queuing Formula” by Little, J. D. C. (1961), encapsulates this groundbreaking concept, known as Little’s Law.
In this context, the formulas utilized in both solutions stand as equivalent representations, illustrating the principles of Little’s Law:
WIP = Throughput x Lead time
<=>
Lead Time = WIP x Cycle Time
Parameter Exploration: WIP, Throughput, Cycle Time, and Lead Time
Here are the definitions for these equations’ parameters:
- lead time is the time between the initiation and delivery of a work item. It is measured by the elapsed time. E.g.: 2 years.
- cycle time if the frequency or time interval when work items are completed. It is measured by the amount of time per unit. E.g.: 2 months per bottle.
- throughput is the rate at which items are passing through the system. It is a measure by units per period of time. E.g.: 6 bottles per year.
- WIP – Work in progress; the number of work items in the system. Work that has been started, but not yet completed. It is a measure by units. E.g.: 12 bottles.
These parameters address distinct questions:
- How long? (Lead time) – representing the duration from initiation to completion.
- How frequent? (Cycle time) – indicating the time between successive occurrences.
- How many? (WIP) – denoting the quantity of work items in progress.
- How fast? (Throughput) – measuring the rate of items moving through the system.
Although these formulas are intuitively reasonable, it’s quite a remarkable result. And this is the main theorem in the Queuing Theory, which is also known as Little’s Law (It was described by John Little in 1961):
The average number of work items in a stable system is equal to their average completion rate, multiplied by their average time in the system.
The average completion rate can be represented by either throughput, or its inverse, average cycle time. This duality is shown at problem statements A and B. These equivalent statements are made in terms of, respectively, throughput and average cycle time.
I don’t know about you, but before digging into Lean, I was a little confused by Throughput and cycle time (and I did not measure it). I hope this blog post you a simple way to understand and explain it. I also hope more people start measuring such important parameters (I can’t believe I did not use these before going Lean!).
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Navigating the Confusion: Cycle Time vs. Lead Time
In the realm of software development, distinguishing between cycle time and lead time often sparks confusion. Many individuals assert that cycle time denotes the duration for a single task, such as developing a user story, whereas lead time represents the total time from task initiation to delivery, encompassing all tasks within a process.
The Significance of Context: Lead Time vs. Cycle Time
Here’s the twist: lead time considers all tasks involved, whereas cycle time zooms in on just one task. The confusion escalates when explanations present lead time and cycle time for a singular task, often visually depicted as the image below.
typical drawing for lead time and cycle time in SW development
But herein lies the dilemma: the broader context is crucial. For instance, if you go back to the problem statements above and consider a scenario with a Work In Progress (WIP) of 1, both lead time and cycle time might appear similar: 2 months (lead time) and 2 months for a bottle (cycle time). People usually say “2 months” for both, because they are dealing with only one bottle (I believe this adds to the confusion as both lead time and cycle time then have the same unit, time elapsed).
Examining the image above while considering a Work In Progress (WIP) of 1 reveals a crucial insight: when WIP is 1, the moment a work request is created, the work starts. Consequently, lead time coincides with cycle time.
The confusion arises when WIP exceeds 1. In such scenarios, cycle time and lead time differ, assuming some elapsed time between the work request is created and the team starts working on it. If you depict both lead time and cycle time as lines (similar to the image above), lead time will extend further than cycle time, highlighting the the time elapsed between the work request is created and the work starts.
The Role of Little’s Law: Understanding the Link
To unravel this confusion, I turn to Little’s Law, a cornerstone in queuing theory. It illuminates the relationship between cycle time and throughput, the latter being the inverse of cycle time. Throughput, expressed as work items per time period, provides a clearer understanding. For instance, saying “I drink 6 bottles per year” (throughput) is far more intuitive than explaining “I finish a bottle every two months” (cycle time). On the problem statement above, I consider option A easier to explain.
My Strategy for Clarifying Confusion: WIP, Throughput, and Lead Time
In practice, when I encounter this confusion in a team I am working with, I avoid using the term “cycle time”, instead, I Will use the terms and focus on Work In Progress (WIP), Throughput, and Lead Time. More important than the nuances of these terms is understanding the dynamics of the system. It’s about grasping the flow and efficiency of the entire process, ensuring a comprehensive perspective in the workflow management.
article updated on September 29th 2023
