{"id":146,"date":"2011-08-19T20:02:00","date_gmt":"2011-08-19T20:02:00","guid":{"rendered":"https:\/\/caroli.org\/en\/little-law-cycle-time-and-throughput\/"},"modified":"2023-09-29T09:03:25","modified_gmt":"2023-09-29T12:03:25","slug":"little-law-cycle-time-and-throughput","status":"publish","type":"post","link":"https:\/\/caroli.org\/en\/little-law-cycle-time-and-throughput\/","title":{"rendered":"Little Law, lead time, cycle time and throughput"},"content":{"rendered":"<p>In this blog entry, we explore the intriguing world of Little&#8217;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&#8217;s dive into the intricacies of these concepts.<\/p><div id=\"ez-toc-container\" class=\"ez-toc-v2_0_89 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Sum\u00e1rio<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/caroli.org\/en\/little-law-cycle-time-and-throughput\/#The_Whisky_Analogy_Setting_the_Stage\" >The Whisky Analogy: Setting the Stage<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/caroli.org\/en\/little-law-cycle-time-and-throughput\/#Problem_Statements_A_and_B_for_exemplifying_Little_Law\" >Problem Statements A and B for exemplifying Little Law<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/caroli.org\/en\/little-law-cycle-time-and-throughput\/#Solutions_Unveiled_Two_Paths_to_the_Same_Answer\" >Solutions Unveiled: Two Paths to the Same Answer<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/caroli.org\/en\/little-law-cycle-time-and-throughput\/#Parameter_Exploration_WIP_Throughput_Cycle_Time_and_Lead_Time\" >Parameter Exploration: WIP, Throughput, Cycle Time, and Lead Time<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/caroli.org\/en\/little-law-cycle-time-and-throughput\/#The_Cumulative_Flow_Diagram_book\" >The Cumulative Flow Diagram book<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/caroli.org\/en\/little-law-cycle-time-and-throughput\/#Navigating_the_Confusion_Cycle_Time_vs_Lead_Time\" >Navigating the Confusion: Cycle Time vs. Lead Time<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/caroli.org\/en\/little-law-cycle-time-and-throughput\/#The_Significance_of_Context_Lead_Time_vs_Cycle_Time\" >The Significance of Context: Lead Time vs. Cycle Time<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/caroli.org\/en\/little-law-cycle-time-and-throughput\/#The_Role_of_Littles_Law_Understanding_the_Link\" >The Role of Little\u2019s Law: Understanding the Link<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/caroli.org\/en\/little-law-cycle-time-and-throughput\/#My_Strategy_for_Clarifying_Confusion_WIP_Throughput_and_Lead_Time\" >My Strategy for Clarifying Confusion: WIP, Throughput, and Lead Time<\/a><\/li><\/ul><\/nav><\/div>\n\n\n<h2><span class=\"ez-toc-section\" id=\"The_Whisky_Analogy_Setting_the_Stage\"><\/span><strong>The Whisky Analogy: Setting the Stage<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>While sitting at my dining table I was thinking about a way to explain <strong>Little Law<\/strong>, <strong>lead tine<\/strong>, <strong>cycle time<\/strong> and <strong>throughput<\/strong>. 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.<\/p>\n<p><a href=\"https:\/\/1.bp.blogspot.com\/-oRKnp2MKNAU\/Tk7CmQaPTZI\/AAAAAAAABfg\/vetafqON-os\/s1600\/little-law-bar-analogy.JPG\" target=\"_blank\" rel=\"noopener\"><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/-oRKnp2MKNAU\/Tk7CmQaPTZI\/AAAAAAAABfg\/vetafqON-os\/s320\/little-law-bar-analogy.JPG\" alt=\"\" border=\"0\" \/><\/a><\/p>\n<h2><span class=\"ez-toc-section\" id=\"Problem_Statements_A_and_B_for_exemplifying_Little_Law\"><\/span><strong>Problem Statements A and B for exemplifying Little Law<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Let&#8217;s begin with two problem statements, both similar was to look at the same situation.<\/p>\n<p><span style=\"text-decoration: underline;\"><strong>Problem Statement A<\/strong>:<\/span> 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?<\/p>\n<p>Or, stating the same problem in a different way:<\/p>\n<p><span style=\"text-decoration: underline;\"><strong>Problem Statement B<\/strong>:<\/span> 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?<\/p>\n<p>From the problem statements I can get the following parameters:<\/p>\n<p>The inventory or <strong>WIP<\/strong> is 12 bottles. (Problem statement A and B)<\/p>\n<p><strong>Throughput<\/strong> is 6 bottles per 12 months (Problem statement A)<\/p>\n<p><strong>Average Cycle tim<\/strong>e is 2 months per bottle(Problem statement B)<\/p>\n<p>And the question is the average lead time<\/p>\n<p>I will solve the problem two ways:<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Solutions_Unveiled_Two_Paths_to_the_Same_Answer\"><\/span><strong>Solutions Unveiled: Two Paths to the Same Answer<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><span style=\"text-decoration: underline;\"><strong>Solution 1:<\/strong><\/span><\/p>\n<p><strong>WIP<\/strong> = <strong>Throughput<\/strong> x <strong>Average Lead Time<\/strong><\/p>\n<p>12 bottles = 6 bottles \/12 months x Average Lead Time,<\/p>\n<p>Therefore, Average Lead Time = 24 months<\/p>\n<p><span style=\"text-decoration: underline;\"><strong>Solution 2:<\/strong><\/span><\/p>\n<p><strong>Average Lead Time<\/strong> = <strong>WIP<\/strong> x <strong>Average Cycle Time<\/strong><\/p>\n<p>Average Lead Time = 12 bottles x 2 months\/bottle<\/p>\n<p>Therefore, Average Lead Time = 24 months<\/p>\n<blockquote>\n<div><span lang=\"EN-US\">\u201cThe average number of work items in a stable system is equal to their average completion rate, multiplied by their average time in the system.\u201d ~ <i>John Little, 1961<\/i><\/span><\/div>\n<\/blockquote>\n<p>&#8220;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.&#8221; This profound wisdom, articulated by John Little in 1961, forms the essence of Little&#8217;s Law, a fundamental theorem in queuing theory. The text above, sourced from &#8220;A Proof for the Queuing Formula&#8221; by <a href=\"https:\/\/en.wikipedia.org\/wiki\/John_Little_%28academic%29\" target=\"_blank\" rel=\"noopener\">Little, J. D. C. (1961),<\/a> encapsulates this groundbreaking concept, known as Little\u2019s Law.<\/p>\n<p>In this context, the formulas utilized in both solutions stand as equivalent representations, illustrating the principles of Little&#8217;s Law:<\/p>\n<div style=\"text-align: center;\">\n<blockquote><p><b>WIP = Throughput x Lead time <\/b><\/p>\n<p>&lt;=&gt;<\/p>\n<p><strong>Lead Time = WIP x Cycle Time<\/strong><\/p><\/blockquote>\n<\/div>\n<h2><\/h2>\n<h2><span class=\"ez-toc-section\" id=\"Parameter_Exploration_WIP_Throughput_Cycle_Time_and_Lead_Time\"><\/span><strong>Parameter Exploration: WIP, Throughput, Cycle Time, and Lead Time<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Here are the definitions for these equations\u2019 parameters:<\/p>\n<ul>\n<li><strong>lead time<\/strong> is the time between the initiation and delivery of a work item. It is measured by the elapsed time. E.g.: 2 years.<\/li>\n<li><strong>cycle time<\/strong> 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.<\/li>\n<li><strong>throughpu<\/strong>t 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.<\/li>\n<li><strong>WIP<\/strong> \u2013 Work in progress; the number of work items in the system. Work that has been started, but not yet completed.\u00a0 It is a measure by units. E.g.: 12 bottles.<\/li>\n<\/ul>\n<p>These parameters address distinct questions:<\/p>\n<ul>\n<li><strong>How long?<\/strong> (Lead time) &#8211; representing the duration from initiation to completion.<\/li>\n<li><strong>How frequent?<\/strong> (Cycle time) &#8211; indicating the time between successive occurrences.<\/li>\n<li><strong>How many?<\/strong> (WIP) &#8211; denoting the quantity of work items in progress.<\/li>\n<li><strong>How fast?<\/strong> (Throughput) &#8211; measuring the rate of items moving through the system.<\/li>\n<\/ul>\n<p>Although these formulas are intuitively reasonable, it&#8217;s quite a remarkable result. And this is the main theorem in the <strong>Queuing Theory<\/strong>, which is also known as <strong>Little\u2019s Law<\/strong> (It was described by John Little in 1961):<\/p>\n<blockquote><p>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.<\/p><\/blockquote>\n<p>The average completion rate can be represented by either <strong>throughput<\/strong>, or its inverse, <strong>average cycle time<\/strong>. This duality is shown at problem statements A and B. These equivalent statements are made in terms of, respectively, throughput and average cycle time.<\/p>\n<p>I don\u2019t 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\u2019t believe I did not use these before going Lean!).<\/p>\n<h2><span class=\"ez-toc-section\" id=\"The_Cumulative_Flow_Diagram_book\"><\/span>The Cumulative Flow Diagram book<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u201cFlow is so important to managing modern work and enabling customer satisfaction. The Cumulative Flow Diagram is very efficient: it integrates a lot of information in a single picture. People often struggle to interpret and master the usage of CFDs. Paulo\u2019s book delivers step-by-step guidance to maximize your understanding and demystify this important tool.\u201d DAVID J. ANDERSON, author of the Kanban: Successful Evolutionary Change for Your Technology Business and several other books<\/p>\n<div id=\"attachment_1613\" style=\"width: 310px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-1613\" class=\"size-medium wp-image-1613\" src=\"https:\/\/caroli.org\/en\/wp-content\/uploads\/sites\/5\/2015\/06\/cfd-flow-parameters-300x225.jpg\" alt=\"\" width=\"300\" height=\"225\" srcset=\"https:\/\/caroli.org\/en\/wp-content\/uploads\/sites\/5\/2015\/06\/cfd-flow-parameters-300x225.jpg 300w, https:\/\/caroli.org\/en\/wp-content\/uploads\/sites\/5\/2015\/06\/cfd-flow-parameters.jpg 960w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><p id=\"caption-attachment-1613\" class=\"wp-caption-text\">CFD and flow parameters<\/p><\/div>\n<p>Explore the transformative potential of the Cumulative Flow Diagram, a vital tool for enhancing workflows. Capturing the essence of this post and the intriguing tale of my whisky bar, I&#8217;ve wrote a concise yet comprehensive book on flow parameters and the Cumulative Flow Diagram. Delve into its pages to gain insights into workflow management and this powerful tool. Interested? Check it out!<\/p>\n<div id=\"attachment_16597\" style=\"width: 253px\" class=\"wp-caption alignnone\"><a href=\"https:\/\/caroli.org\/en\/livro\/cfd\/\" target=\"_blank\" rel=\"noopener\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-16597\" class=\"wp-image-16597 size-medium\" src=\"https:\/\/caroli.org\/en\/wp-content\/uploads\/sites\/5\/2022\/06\/book-cumulative-flow-diagram-243x300.jpg\" alt=\"cumulative flow diagram book cover\" width=\"243\" height=\"300\" \/><\/a><p id=\"caption-attachment-16597\" class=\"wp-caption-text\">book available on Amazon<\/p><\/div>\n<h2><span class=\"ez-toc-section\" id=\"Navigating_the_Confusion_Cycle_Time_vs_Lead_Time\"><\/span><strong>Navigating the Confusion: Cycle Time vs. Lead Time<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>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.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"The_Significance_of_Context_Lead_Time_vs_Cycle_Time\"><\/span><strong>The Significance of Context: Lead Time vs. Cycle Time<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Here&#8217;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.<\/p>\n<div id=\"attachment_212248\" style=\"width: 479px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-212248\" class=\"wp-image-212248 size-full\" src=\"https:\/\/caroli.org\/en\/wp-content\/uploads\/sites\/5\/2011\/08\/lead-time-vs-cycle-time-sw.png\" alt=\"lead time and cycle time\" width=\"469\" height=\"258\" srcset=\"https:\/\/caroli.org\/en\/wp-content\/uploads\/sites\/5\/2011\/08\/lead-time-vs-cycle-time-sw.png 469w, https:\/\/caroli.org\/en\/wp-content\/uploads\/sites\/5\/2011\/08\/lead-time-vs-cycle-time-sw-300x165.png 300w\" sizes=\"(max-width: 469px) 100vw, 469px\" \/><p id=\"caption-attachment-212248\" class=\"wp-caption-text\">typical drawing for lead time and cycle time in SW development<\/p><\/div>\n<p>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 &#8220;2 months&#8221; 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).<\/p>\n<p>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.<\/p>\n<p>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.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"The_Role_of_Littles_Law_Understanding_the_Link\"><\/span><strong>The Role of Little\u2019s Law: Understanding the Link<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>To unravel this confusion, I turn to Little&#8217;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 &#8220;I drink 6 bottles per year&#8221; (throughput) is far more intuitive than explaining &#8220;I finish a bottle every two months&#8221; (cycle time). On the problem statement above, I consider option A easier to explain.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"My_Strategy_for_Clarifying_Confusion_WIP_Throughput_and_Lead_Time\"><\/span><strong>My Strategy for Clarifying Confusion: WIP, Throughput, and Lead Time<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>In practice, when I encounter this confusion in a team I am working with, I avoid using the term &#8220;cycle time&#8221;, \u00a0instead, 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&#8217;s about grasping the flow and efficiency of the entire process, ensuring a comprehensive perspective in the workflow management.<\/p>\n<p><strong>\u00a0<\/strong><\/p>\n<p>article updated on September 29th 2023<\/p>\n<p><!-- Begin MailChimp Signup Form --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>In this blog post, the concepts of Little&#8217;s Law, lead time, cycle time, and throughput are explored through an analogy involving whisky bottles. Two problem statements concerning whisky consumption and purchases are presented, leading to the derivation of key parameters such as work in progress (WIP), throughput, cycle time, and lead time. The post offers two solutions that highlight the equivalence of the formulas employed, simplifying intricate concepts in queuing theory for readers. Additionally, the Cumulative Flow Diagram is introduced as an efficient tool for visualizing and managing work processes. <\/p>\n","protected":false},"author":1,"featured_media":818,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_et_pb_use_builder":"","_et_pb_old_content":"","_et_gb_content_width":"","footnotes":""},"categories":[2114],"tags":[772,692,746,756,806],"inception_activities":[],"colaboradores":[],"class_list":["post-146","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-kanban-en","tag-cycle-time-en","tag-kanban-en","tag-lead-time-en","tag-lean-en","tag-little-law-en"],"_links":{"self":[{"href":"https:\/\/caroli.org\/en\/wp-json\/wp\/v2\/posts\/146","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/caroli.org\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/caroli.org\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/caroli.org\/en\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/caroli.org\/en\/wp-json\/wp\/v2\/comments?post=146"}],"version-history":[{"count":0,"href":"https:\/\/caroli.org\/en\/wp-json\/wp\/v2\/posts\/146\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/caroli.org\/en\/wp-json\/wp\/v2\/media\/818"}],"wp:attachment":[{"href":"https:\/\/caroli.org\/en\/wp-json\/wp\/v2\/media?parent=146"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/caroli.org\/en\/wp-json\/wp\/v2\/categories?post=146"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/caroli.org\/en\/wp-json\/wp\/v2\/tags?post=146"},{"taxonomy":"inception_activities","embeddable":true,"href":"https:\/\/caroli.org\/en\/wp-json\/wp\/v2\/inception_activities?post=146"},{"taxonomy":"colaboradores","embeddable":true,"href":"https:\/\/caroli.org\/en\/wp-json\/wp\/v2\/colaboradores?post=146"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}