When discussing lean math with other folks, I often get some less than optimal responses. Of course, much of the time it’s probably me!

In any case, this is how I would characterize the more non-value-adding responses to the subject. 

• Apoplectic. You know, the math anxiety induced stroke. Some people would be more than happy living in a math-free world. The mere mention of numbers and formulas can lead to hyper-ventilation, lack of focus, and non-productive hand-wringing. Relax, you probably won’t be using this math to save any lives or deliver any babies. 
• Catatonic. As in an eyes glazed over kind of stupor. This stupor can be induced by either boredom (math ain’t too exiting) or it can be a coping mechanism that convincingly signals to co-workers that they better take this one because my brain has seized up. Often the catatonic state is preceded or followed by apoplexy.
• Obsessive. Some folks get into the math so much that they lose any notion of balance between theory and reality. Lean-oriented math is a vehicle for improvement. It is not the end game…and the best application of “belts” is to hold up one’s pants.  
• Contentious. And then there are those who would like to argue every aspect of the math, often not because it matters, but because it’s a venue to establish intellectual superiority. During these arguments (or the contentious one’s monologue), the other people tend to look around for possible escape routes.

My simple suggestion to everyone is two-fold: 1) never stray from lean principles, and 2) get your hands dirty.

Indeed, lean principles are the foundation. You can’t trump things like respect, humility, flow, pull, stop and fix, etc.

The notion of experimentation and application reflected in the figure below equates to getting your hands dirty.

Lean Math in Context

Certainly, some lean math formulas can be intimidating, we can’t get trapped into inactivity – the old analysis paralysis. Lean is largely about learning by doing. This is where, depending upon the implementation risk, trystorming and simulation are critical strategies for moving forward.

So, for example, if you’re looking to implement a mixed model production kanban, it probably makes sense to do some table top simulations (with proxy kanban cards), and run through several weeks of actual historical demand…in excruciating detail as you test supermarket levels, stock-outs, emergency kanbans, impacts of changeovers, unplanned downtime, etc. Try to see when and where the system breaks down…then make adjustments and do it again and again (think plan-do-check-act, PDCA).

When the implementation risk is less significant, like developing a new performance metric, the trystorming or simulation may be close to zero. Put it out there and apply PDCA in real time.

“Use” the math. As fellow lean practitioners, we’re all looking to effect continuous improvement. A 5% or 10% improvement today is better than a 80% improvement at some unspecified time in the future.

So, in a word, get over your lean math phobias, have some fun and never violate lean principles.

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Here’s some often overlooked and misunderstood value stream mapping math.

The lead time ladder has two levels or “rungs.” The bottom rung is the process or processing rung on which the relevant process time is dropped down. This is usually pretty straightforward…unless there is a split or branch in the material, service or knowledge flow within the value stream.

For example, after a fabrication process, the material may flow 35% of the time to a coating process and then to an assembly process, while 65% of the time the coating process is skipped altogether. The value stream map essentially reflects a process time for a hybrid (or weighted average) product or service, in such a situation. Accordingly, the process times for these branches must be apportioned by the split %, as illustrated in the figure below.

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The operator balance chart, also known as a percent load chart, operator loading diagram, cycle time/takt time bar chart, or line balance analysis graph, provides the lean practitioner with insight into how equalized operation time is among the workers within a given process, line or cell. The line balance rate (LBR), and the related line balance loss rate (which is simply 100% minus the LBR), quantifies how well or poorly the line is balanced.

A lack of line balance routinely causes the waste of waiting and/or overproduction. It can also prompt over-processing during which operators, rather than engage in the blatant waste of waiting, conduct “apparent work.” Line imbalance is an enemy of continuous flow.

Some may ask, “What the heck do I do with this?” While there is not necessarily a magical LBR “bogey,” it’s definitely useful when developing standard work and comparing different balance scenarios.

Consider LBR a simple analytical tool. Use it when it makes sense.

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 Many folks use the terms efficiency and productivity interchangeably.

 They are not interchangeable. They are not equivalent.

 Heck, they’re not even synonyms – even though Thesaurus.com thinks so.

Technically, productivity is a ratio of (good) outputs to inputs and efficiency is the ratio of actual output to standard output. Lean practitioners are typically and more appropriately concerned about productivity. As the famous Art Byrne, former CEO of Wiremold, said, “Productivity = Wealth.”  

BUT, in this post, we are talking about efficiency! And it’s important to understand the basic math around efficiency.

Efficiency is the ratio, typically reflected as a percentage, of actual output to the standard expected output. The measurement therefore provides insight into how well a resource(s) is performing relative to a standard.

Lean practitioners know that traditional standards are often not well maintained and do not always closely reflect reality. Accordingly, efficiency measurements may provide an inaccurate view of performance and may mask improvement opportunities. Standard work rigor, integrated with kaizen, should help reduce these risks and appropriately focus the organization.

Efficiency ratios can be categorized as follows (APICS Dictionary, 13^th ed.):

1. actual units produced or processed to the standard rate expected within a time period (hour, day, week, etc.),
2. standard hours produced or “earned” compared to actual hours worked, and
3. actual dollar volume of output to a standard dollar volume of output within a time period.

The math follows:

Related post: Productivity (and not efficiency)

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Honestly, the last bit of formal and substantive math that I worked with was back in college. Many, many years ago, I received a B.S. in Mathematics, but other than the diploma, there is little physical or intellectual (!!) evidence that would support this reality.

My former classmates might say the same was true way back when. My kids? Well, they used to hesitate before asking me to help them with their math homework.

…Which is exactly why I associate with really smart folks like my Lean Math^TM blog co-founders Larry Loucka and Michael O’Connor (a.k.a. Dr. Mike – seems he has a Ph.D. in Physics).

In any event, it’s tough to write about math without using mathematical symbols and notation. I know, you’re probably on the edge of your seat right about now. This is going to get really, really exciting, right?!

No, obviously, it’s not. But, we need to cover this sooner or later. This post will find its rightful place in the archives and the symbols are permanently posted under the “Symbols” menu tab.

So, without further ado, please check out this very cool and oh, so unique table below.

As you most likely noted in the table, certain variables were referenced, for example  x, a, b, A, and B. Most Lean Math^TM entries have at least one formula with multiple variables. These variables, virtually always independent variables in that they are inputs into a system, represent a value that may change within the scope of the problem or operation. For example, work content (W_c) and takt time (T_t) within the optimal staffing model are independent variables. They are what they are.

Typically variables have single-symbol names, with constants from the beginning of the alphabet (e.g., a, b, and c) and variables from the end (e.g., t, x, y, and z). You can thank the 17th French philosopher and mathematician, Rene Descartes, for that. The single symbol names are usually italicized and are often lower case. Oh, and upper case variables are traditionally used for random variables within probability and statistics. All that we can say is that we tried our best to follow these conventions, but we’re pretty sure that we broke, and will break, more than a few rules here and there.

Honestly, the easiest notation many times is no notation. For example:

Who can’t understand that?!

The problem is that more complicated formulas end up being way too long for the printed page. This requires very tiny font and/or multiple lines on a page. Not good (according to editors)!

Furthermore, there are certain variables that are used relatively frequently with this blog. It seems that a variable such as T_t for takt time, may be the least waste way. Of course, we define our variables within every post that contains a formula.

As you’ll see we have tried to keep most variables to one letter with a subscript to further identify it – like the “T” for time and “t” for takt. Of course, this convention is not always possible and not always prudent. For example, everyone knows “WIP” as work-in-process inventory. We have no desire to needlessly invent brand new variables!

Another, occasional departure from convention is the double subscript, for example I_cc is inventory carrying cost…or did we change that to I_c?! Our apologies if we have offended any math purists.

Ok, there you have it. If you made it through this post, thank you for your perseverance! Now, let’s do some math!

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Container capacity (C_c) is one of the four basic variables within the generic kanban sizing calculation. However, C_c is often NOT treated as variable, but more as a constant, pre-determined quantity, especially if the lean practitioner seeks to use existing supplier packaging, reusable dunnage, standard bin sizes or racks, etc.

Often that is the best, least waste way. Although, sometimes it is not prudent from an inventory management and/or ergonomic perspective.

Oversized bins may facilitate the waste of excess stock on hand and expose an operation to shelf-life expiration risk, damage, and obsolescence. High container capacities can also mean heavy, large, and/or unwieldy containers and thus increase the risk of ergonomic injuries and require expensive, large, and clumsy ways of moving the containers.   

So, occasionally, it makes sense to “solve” for C_c, primarily if the lean practitioner seeks to create a two bin system.

If the lean practitioner seeks to limit C_c for ergonomic reasons, the following formula can be applied.

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The seminal book on lean, The Machine that Changed the World, spent many words, tables, and figures on the subject of productivity (as well as, of course, quality).

Why?

Productivity is one of the critical few measures that reflect the “leanness” of a process, value stream or enterprise. It captures how effectively an organization uses its resources, and it’s usually a meaningful way to compare performance over time and between entities.

Productivity is the ratio between the outputs of goods or services and the inputs applied for the purpose of that output. There are two typical applications of this ratio – single-factor productivity and multi-factor productivity. Labor is often the single factor and is referred to as labor productivity. Another popular single factor is machine productivity.

Labor productivity captures the output per labor input. Outputs are often units, but can also be reflected in the dollar value of the labor. Multi-factor productivity, as the name implies, takes into account multiple inputs; typically labor and resources such as capital equipment, energy and material. The common unit of measurement for multi-factors is almost exclusively dollars.

Example productivity ratios include:

• units per labor hour
• units per person per hour
• units per labor dollar
• sales per person
• units per machine hour
• units per square foot
• sales per square foot
• total processing cost per unit

The number of different productivity measurement is limited only by the imagination. But, like anything, the measurement must be pragmatic and help drive the proper lean behavior with a focus on period over period improvement within the process, value stream and enterprise.

The formula and ABC Company example(s) follow:

Some other things to think about:

• Understanding productivity is important. However, lean practitioners also distinguish between local and total (think “system”) productivity. So, while a cell or department’s productivity level is important, the total value stream is even more critical.
• Don’t be fooled! Understand the difference between real and apparent productivity:

• When comparing productivity rates between lines, cells, value stream, locations, etc. it is important to understand relative work content. If work content varies substantially between areas, the productivity comparison may be misleading and require the use of common units.
• “Underutilized” inputs can distort productivity calculation results. For example, abnormally low demand can cause productivity to plummet. In such a situation, it may make sense to also calculate labor productivity only using the hours which the operators were working (other hours may have been heavily invested in cross-training and improvement activities).

Related post: Efficiency (and not productivity)      

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Every Part Every Interval, also known as EPEI or EPEx, represents the frequency that different parts are produced or services provided within a fixed repeating schedule. This fixed repeating schedule is often graphically portrayed, for training purposes and as a scheduling visual control, as a wheel, with the different products represented by alphas (A, B, C…) and the wheel indexed clockwise to follow the intended sequence.

EPEI is typically reflected in days or partial days and represents the time interval between successive complete wheel revolutions or runs. The lean practitioner seeks to make EPEI as small as possible (all the way down to shift, hour, or pitch) in order to reduce inventory and compress lead time. This can be accomplished by means of reducing changeover time, reducing the number of different parts (and thus the number of set-ups), reducing cycle times, and/or reducing the volume of products loaded on a particular machine. Obviously, an integral element of the EPEI calculation is available time for changeovers.

The EPEI concept is used to size, via the replenishment lead time variable, pattern production kanban and triangle kanban (using the product specific lot size method). Note that typically only pattern production kanban are replenished strictly within a fixed repeating sequence. Even within pattern production kanban systems the lot sizes produced will vary to accommodate the actual replenishment quantity needed.

Keep in mind that not all parts are necessarily created equal as the EPEI concept prescribes. For example, replenishment strategies may call for certain products to be made every day, while others made weekly, bi-weekly or monthly, based upon demand dynamics, inventory level considerations, shelf life, etc. That’s when we get into changeover distribution discussions (for another time).

Some EPEI math follows:

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Machine cycle time (T_cm) represents the actual time it takes for one machine to complete all of its operations on one piece, product, patient, file, etc. It is applicable for both single piece and batch processing. Unlike effective machine cycle time, T_cm excludes load and unload time as well as any changeover time.

While T_cm does not reflect operator time, it is critical to understand the relationship between the operator and machine within time and space. Tools such as standard work combination sheets facilitate that understanding, may help identify opportunities for jidoka and provide an important comparison of operator cycle time and takt time.

As with any cycle time measure, machine cycle time should be confirmed through direct observation of multiple cycles. Lean practitioners need to identify and understand significant machine cycle time variation and address appropriately.

Related posts: The Cycle Time Family, Time

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Recently a reader posed the following value stream mapping lead time related question(s). My experience, after facilitating more value stream mapping activities than I care to remember, is that it’s not an uncommon question. In fact, it’s a very good question.

I provided a quick answer…supplemented by a very sophisticated graphic (recently enhanced, in red, based on a comment from Sandor).

Q: Say you have a value stream map that after Process A is complete, can either go to B, C, OR D and then no matter the process, continue to E from there. How do you go about adding up lead time? Do you just take the longest of those three times or an average?

A:  In such a situation, lead time, as reflected on the “top rung” of the lead time ladder, is based upon the inventory in the system. The lead time on each rung is typically calculated by dividing the average daily demand by the inventory count associated with the triangle (typically) above that rung. This will provide lead time in terms of days or fractions of a day. (There are other methods, but this one is probably the most simple.)

So, the question is whether there is inventory before B, C, and/or D and how much. Then, calculate the lead time related to each inventory triangle. See the attached picture for a quick example.

Related post: Value Stream Mapping Math: Lead Time Ladder Process “Branch”

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Pitch is a representation of takt image – a visual and often audible management timeframe that lean practitioners use to pace and monitor value stream performance. It is typically driven by, and linked to, a value stream or line’s pacemaker process. Pitch performance is routinely tracked and reinforced with plan vs actual charts (a.k.a. production analysis boards), digital displays, lines that are “pulsed” or indexed every time interval, etc.

The principle behind the math is around early identification and timely reaction to problems. Accordingly, pitch should be matched to the organization’s (hopefully, ever improving) capability to react to problems. If pitch is too short, then it may not invite anything other than frustration. If pitch is too long, then problems will fester and grow before they are flagged.

Essentially, pitch’s takt image is a reflection of takt time and what we’ll call a “pace multiple.” The pace multiple is often, but not always, a release, conveyance, or shipment quantity. It is an oversimplification to say it is always a packout quantity, although that is a good place to start.

Sometimes, pace multiple selection is more an application of good, pragmatic lean judgment. In other words, when things like release and conveyance quantities are either too big or small (perhaps the product is very large or cumbersome) to provide a useful takt image or are just not applicable (like in many non-manufacturing value streams), the lean practitioner may need to “back into” a useful interval – like 30 or 60 minutes.

While pitch is typically a multiple of takt time, that is not always practical. In some instances, when takt time is extremely long, such as hours, days or even weeks, pitch is appropriately a fraction of takt. In this situation, it is sometimes referred to as “inverse pitch,” (P_i) and ensures that the management time frame is finite enough to provide workers and leadership timely feedback.

Some math for pitch and inverse pitch follows:

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Work content (W_c) represents total operator cycle time or, if multiple operators, the sum of operator cycle times to perform a specific process(es) or sub-process(es). The scope of human work, including both value-added and non value–added activities, may encompass a complete value stream or only a portion of it. For example, the lean practitioner may speak of the work content to check-in and room a patient, assemble a sensor module or process a claim. The term “total work content,” is applied when referencing the work content to build a product in its entirety, completely execute a certain transaction, etc.

As the name implies, the focus is on the work; reflecting the sum total work of ALL people within the subject process(es) or sub-process(es) to complete one cycle. Think about work content as the work, comprised of manual, wait, and walk time, it would take if one person were to execute the entire cycle all by himself. Of course, when one person does do the entire cycle, work content is pretty easy to determine.

Wait time excludes inter-operator waiting. For example, the lean practitioner would not include the time of operator B waiting for operator A to present a sub-assembly within the work content calculation. 

It is important to understand total work content for the purpose of determining optimal staffing levels and to understand work content variation and its implications within a mixed model environment.

The math follows:

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The time observation form, also known as a process study form, is a basic and often-used tool for lean practitioners. Note that here we are talking about the application of the continuous time observation method and not the work sampling method.

The form, in combination with a stop watch, serves multiple purposes, including:

• facilitating direct observation of processes (one form per operator),
• requiring the identification/recording of the smallest observable component tasks and separation of operator and machine time,
• recording component task times (which may sometimes be grouped, if appropriate),
• encouraging observation of multiple cycles to better determine the lowest repeatable cycle times,
• highlighting cycle time variation (with same and different operators) and providing insight into the reasons for variation,
• helping identify and note waste, and
• ultimately, facilitating the development of standard work

 That said, the time observation form requires a little bit of math (and a lot of practice!), particularly if the form is consistent with that used within Toyota. The figure below reflects a traditional time observation form training example, along with some alpha “call-outs” by which the math is explained.

Some things for the lean practitioner to consider:

• The intent of the time observation form typically includes determining the lowest repeatable cycle time and the supporting task times. However, if the lean practitioner is trying to characterize improvement potential he/she may select the shortest elemental times and then kaizen from there.

• Observe an experienced, qualified operator who is not the fastest or slowest. If at all possible, observe multiple operators to gain more insight into cycle time, component tasks, sequence, and opportunity.

• Some people derive component task times by taking the average of the cycles observed. This can be very dangerous in that significant cycle time variations may “pollute” the numbers and thus impair kaizen insight and/or yield insufficient standard work.

• Avoid including out-of-cycle work (i.e., cleaning off a work surface every 30 minutes or every 100 or so parts, occasionally retrieving raw materials for line-side work) as component tasks…unless of course the observation target is the non-cyclical work.

Related posts: The Cycle Time Family, Time

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From my experience, there are a handful of pull system design steps. This post seeks to “simply” outline those steps and some of the math that should be considered.

However, don’t let the brevity of this post mislead you. It isn’t necessarily simple.

We will address more and more of the referenced math through future Lean Math posts.

1. Understand and segment customer (internal or external) demand. The lean practitioner may find the following lean related math useful: average period demand, coefficient of variation, demand segmentation, ABC inventory analysis, and days inventory on hand.
2. Understand supplier (internal or external) reliability, quality and availability. Relevant math includes: operation ratio, on-time delivery,  scrap factor, etc.
3. Select best pull system type – supermarket pull, sequential pull, or a hybrid. Not a lot of explicit math here, often this is driven by lean principles and value stream characteristics and value stream and organizational maturity.
4. Understand supplier lead times. The devil is in the detail and the detail includes, but is not limited to: available time for changeovers per period, changeover opportunities per day, changeover distribution, and replenishment lead time.
5. Understand pull system design constraints – working capital, floor and shelf space, shelf life, organizational discipline, etc. The following math may be meaningful: inventory carrying costs, inventory turns, square root law of inventory, and Pick’s theorem (to measure square footage).
6. Select best kanban type (if the decision is kanban). The basic options are production instruction (in-process kanban or batch kanban. If batch, triangle, pattern production, or lot making.) or withdrawal (interprocess or supplier kanban). Does your head hurt yet?
7. Calculate and size the pull system. The typical kanban calculations are based upon average period demand, replenishment lead time, factor of safety (considering both buffer and safety stock requirements), and container capacity. And, there’s math behind this math. For example, there are lead time nuances to consider based upon the type of kanban and there are things to think about when calculating trigger points and FIFO lane sizes.
8. Simulate/test the system. PDCA often includes stock-out analysis math.

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The process capacity sheet, also known as a table of production capacity by process or production capacity chart or process capacity table, is one of the three basic tools for establishing a standard operation. The other tools are the standard work combination sheet and standard work sheet. All three standard operations sheets are populated with data obtained through direct observation (as is the time observation form).

The process capacity sheet, as the name implies, is for the purpose of determining a given process’ capacity for a shift, and thus its ability to meet takt time. This determination is made through the calculation of each process step’s capacity, considering the available time per shift, completion time, and tool change time, and other factors, as required, for each single work piece. The process’ overall capacity is defined by the bottleneck step, which may be addressed through things like changeover time reduction and machine and/or operator cycle time reduction. Some versions of the sheet, like the one below, also provide fields for the number of required operators to satisfy takt time and calculated maximum output.

The figure below shows a populated process capacity sheet, along with alpha “call-outs” by which the math is explained.

 Other related posts: Available Time, Machine Cycle Time

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Little’s Law, named after John D. C. Little and his 1960 queuing proof, characterizes the dynamic relationship between work-in-process inventory (WIP), throughput rate, and lead time within a reasonably stable system. The “system” can be that of a process, cell, or line and can extend to one or more value streams. The Law, like all core lean principles, is universal and applies to all industries.

If the system has fixed capacity, lead time and WIP are proportional, meaning that if there is an increase or decrease in WIP, there is a commensurate impact on lead time, and vice versa. Throughput rate represents the average output of the system per unit of time and may be increased by improving bottleneck utilization and/or bottleneck rate. Lead time is the average time span for each unit to move completely though the system, including all process time and queue time, from its initial introduction to its final completion and release from the system. The “unit” here, can be an assembly, insurance claim, patient, etc.

The math for Little’s Law follows:

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Weighted average cycle time (T_cwa), also known as “average weighted cycle time,” provides a representative average cycle time (T_c) within a mixed model environment. Varied models or services in a given cell, line or work area often have varied work contents due to different steps, duration of steps, sequence of steps, etc. Accordingly, the T_c‘s vary.

T_cwa can be calculated for operator cycle times, machine cycle times and effective machine cycle times. Often T_cwa is presumed to be operator related, but this is not always the case.

As we endeavor to maintain a T_c that is less than or, at most, equal to takt time (T_t), mixed models and their varying work content will likely have T_c‘s for some products or services that are below T_t, while others exceed T_t. T_cwa serves as an average proxy for T_c and can be the same as planned cycle time.

Clearly, change in product or service mix will change T_cwa. As the demand mix shifts to one with a greater proportion of T_c(s) that exceed the average, then T_cwa will approach and may exceed T_t. The lean practitioner must be aware of these dynamics and should proactively address the situation through reducing work content, optimizing balance between operators, adding additional operator(s) or lines, strategically applying/sizing FIFO lanes, etc.

The math follows.

Related posts: The Cycle Time Family, Time, Time Observation Form Math

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The WIP-to-SWIP ratio is a simple comparison of a process, line or cell’s actual work-in-process count versus its standard work-in-process inventory (SWIP). Among other things, a process’ target condition reflects the consistent execution of standardized work, including SWIP maintenance (which is why it should be a leader standard work audit point). No SWIP maintenance, no standardized work adherence. Accordingly, the target WIP-to-SWIP ratio is 1. 

A ratio less than 1 indicates that, at least during the time of the WIP count, the WIP level is insufficient. A ratio greater than 1 reflects a situation in which there is excess WIP. Daily or even more frequent tracking on a run chart or plan versus actual type chart can be incorporated within the natural work team’s visual metrics. Of course, this does not preclude an appropriate andon pull and response. Abnormal conditions should be quickly flagged and the root causes identified and addressed.

Depending upon the potential for normal variation in SWIP, the lean practitioner may want to apply tolerances to determine whether or not there is truly a problem. For example, if a cell’s SWIP is 4 units with strict one piece flow, a WIP count that does not exactly match that target is significantly abnormal. However, a line with 15 units of SWIP, may be “allowed” 15, plus 0, minus 3 units to accommodate normal fluctuation (due to work content variation) because the line has an internal FIFO lane with a maximum level of 5 and a minimum of 2.       

The math follows:

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Heijunka, also known as level-loading, production-leveling or production-smoothing, is a foundational element of the Toyota Production System. It facilitates system stability by addressing workload unevenness (mura) through the leveling of both volume and mix over time, see Figure 1. Heijunka also serves as a pacing mechanism for operations, often reflected in the use of heijunka, leveling, or schedule boxes, which are typically designed using pitch intervals, see separate pitch post.

Successful heijunka reduces lead time, inventory, and worker physical and psychological stress that can accompany fluctuating workloads. Some prerequisites include quick changeovers, capable processes, standardized work (or at least defined work content), good visual management, and a solid understanding of customer demand – volume, mix, and variation, see separate demand segmentation graph post.

Figure 1. Example of volume and mix leveling

The heijunka cycle (C_h) represents a regular, repeatable production sequence to facilitate the leveling of mix. The lean practitioner can readily calculate it using a simple spreadsheet and one or more illustration iterations of the proposed cycle, followed by some real PDCA at the gemba. See Figures 2 and 3, as well as the related formulas. As with the concept of takt time, consider C_h more as a design parameter, than a precise and rigid blueprint for developing the heijunka system.

Figure 2. Example heijunka cycle calculation

Figure 3. Heijunka cycle illustrated

 It bears repeating, don’t sweat the math if the ratios aren’t perfect whole numbers (that only happens in the examples provided by teachers and consultants). Pragmatically round when appropriate and remember that mix is often a dynamic thing. Good, simple and visual heijunka standard work will cover for real-life variation.

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On behalf of Michael O’Connor, Larry Loucka, and myself, I would like to thank you for investing your valuable time this year reading our posts and sometimes sharing your thoughts. We truly appreciate your readership and we hope that we have, in some way, provided assistance in your lean journey.

In that spirit, some basic holiday lean math follows…

 PEACE ON EARTH + GOODWILL = HAPPY HOLIDAYS

I am painfully aware that while the equation is simple, the successful and sustained (mathematical) execution has been eluding humans for a long, long, long time.

Here’s to the sincere hope that you and yours will have a happy and blessed holiday season.

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