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:

**Related posts:** Applied EPEI [guest post], Available Time for Changeovers

## There are 13 Comments

I am currently working on a project trying to establish batch sizes for every part on each machine and others believe a EPEI flow is logical; however, I have a major concern. The demand for a machine varies greatly based one the part. Say the average daily demand by part is like 725 for A 625 for B and 50 for C. It doesn't make since to make Part C every interval when our current changeover times are around 4 hours and the cycle times are about 60 seconds. The standard EPEI calculation says we should have a 18 day batch size based on .66 hours available for changeovers and 12 hours of changeovers required. How could we modify this calculation based on running Part C like once every 2 weeks or several intervals of just A and B?

Hi Justin,

Excellent question. It looks like it may make more sense for you to pursue a triangle kanban (using the universal lot sizing method) or lot making kanban for these batch processes. Of course, knocking down internal changeover time would make life a whole bunch easier for you.

As you have determined, not all parts are created equal and therefore EPEI does not make sense. For example, for the purpose of determining the replenishment lead time (necessary to size lot making kanban), you need to determine the number of changeover opportunities per day ((total available time/day - run time (average daily demand * 60 seconds/piece) - daily planned downtime - avg unplanned downtime)/average changeover time), which you are essentially saying is 0.165 (0.66 hrs/4 hrs). Next, you'll need to determine how to "spend" these changeovers. As you have stated, you can do 3 changeovers every 18 days...or 5 changeovers every 30 days, which you could spend so that you changeover to part A every 15 days (that's 2 out of the 5 changeover opportunities every 30 days), part B every 15 days (2 out of 5), and part C every 30 days (1 out of 5).

There's a lot more math for proper kanban sizing, but I hope the thoughts above help.

Best regards,

Mark

I think that EPEI is the single least understood (and therefore the least used) but among the most powerful of lean metrics. It really is key for high mix/low volume value streams especially when a process is capacity constrained and changeovers are not trivial. Obviously if takt > cycle time + changeover then EPEI is meaningless since you can afford to change over for every part. Once that's not the case, then EPEI is key.

I've used a kanban sizing calculation that's based on EPEI which reflects the fact that EPEI is directly related to how much buffer inventory must be maintained at a process. I've also used EPEI as part of determining minimum batch sizes.

With some value streams, the number of members in the product family far exceeds the number of parts that you would ever produce in any normal period and the EPEI is better considered as "Every Ordered Part Every Interval". For example, if you have 2200 products available but in an average period you get between 250 and 400 different parts ordered, it would never be correct to calculate EPEI on the basis of orders for all 2200 parts. In these situations EPEI fluctuates with product mix and volume across periods. So what I've done is set a "Targeted EPEI" at a somewhat realistic period (say a week), and then take time slices of actual history to see how EPEI varies from lower volume weeks to higher volume weeks. Then we can refine the Target EPEI to be able to manage within a desired level of mix and volume and size supermarkets and kanbans accordingly. If course there still needs to be a buffer plan to protect customer shipments even with somewhat abnormally high demand however that should be a quantative trade-off between how much we are willing to tie up in capital to buffer and how much inventory variation we will support within our quoted lead time.

Phil

Phil,

Thanks for the comment and for sharing your excellent insight.

Your "EOPEI" sounds like a strategy for sizing lot making kanban. Essentially, the replenishment lead time used to size the kanban is 1/changeover distribution for the given sku, where changeover distribution is in time units (typically fractions or multiplied of days or weeks, for example 0.2 changeovers/day).

Best regards,

Mark

Eli,

You have the right idea with recalculating the EPEI to dynamically adjust the batch sizes on each rotation. I set a "Planned Interval" as longer term expression of the capacity of the value stream and then set a "calculated EPEI" based on the actual mix and volume of orders for the period. The comparison shows me the capacity impact for the next period. Then we can look at how to use buffers for an oversold period or excess time when a period is undersold. It has to be dynamic. I have software that does this for high mix/low volume value streams.

Phil

Hello, Phil.

Thanks a lot for your comment. As I understand, correct me if I´m wrong, the way you manage is by first setting a sort of "standard" lot sizes that accommodate to a "standard" demand within a time interval. Then real demand comes and you compare it to the standard demand. After that, you make the math and then make the necessary adjustments over the lot sizes to accommodate for the actual demand and the forecasted buffer movements, given the adjusted lot sizes for the interval you are about to start, right? Sounds like a very excelente idea!!!! Is it working good??? I hope it does. Just do not desperate. Sometimes it takes a relative long time to stabilize the production systems and get good results.

You know, as you said in your first comment, there is little interest on EPEI out there. Most of the lot sizing production models look at the problem from the "economic" side (holding costs vs setup costs) but not from the "produce the right lot size to catch up with demand" perspective.

At the end, I have also the feeling like you that EPEI "Every Part Every Interval" has been misunderstood all the way since the beginning from its very name. If anyone wants to sell the idea to the top management should start first from calling it in a different way, like Don Guild did: "Capacity Based Lot Sizing" instead of EPEI. EPEI sounds just like "produce all the models, all the time" which has nothing to do with its potential to be applied in the finite scheduling of production.

Hi Eli,

Dynamic EPEI? That's an interesting concept. As with most things within lean, it would be instructive to simulate how this would work using actual historical data. For example, "running" it (tabletop) using the last few weeks of demand and artifacts representing the EPEI wheel, parts, etc.

Some things to consider - Is the demand all firm? In other words, is it all MTO? Or is it all MTS? Or is it a hybrid, pull system (MTS and MTO)? You say "production targets," so this leads me to believe that this may be all plan (push) and no pull.

You could consider a production pattern kanban. Replenishment in such a model is obviously done in the sequence of the pattern and the production quantity is determined typically by the gap between the current count by SKU and the full kanban size by SKU.

Best regards,

Mark

Good afternoon,

Here is our dilemma:

We are trying to set up a Production Kanban system at a machine center that makes 36 different part numbers. We are familiar with using a Kanban system. Each of the previously mentioned part numbers has a specific set up time and cycle time. We are trying to use EPEI in our Kanban calculations and are greatly confused. Here are our questions:

•How do you account for pack size in your formula?

•Are we using the right logic with employing EPEI?

•If so, how do we calculate EPEI and use it in the Kanban formula in our situation?

•What Kanban formula would you recommend for production Kanban and EPEI?

Thank you greatly for any help you can offer,

Mike Zapata

Hi Mike,

Thanks for the comment. I just posted a new article around pull system design. Please take a look at that first and then if you would like, shoot me an email at mark@leanmath.com and we can continue the conversation.

Best regards,

Mark

At the end, my idea is to realize the possibility for EPEI to be recalculated on every rotation, and by this means, to DYNAMICALLY ADJUST THE BATCH SIZES on every rotation to accommodate production targets for inventory fluctuations too, which at the end, are the ultimate reflection of the stochastic interaction between production and demand. With this, we would not only use EPEI for production system design (kanban determination, inventory normal fluctuation, etc), but for its operation too (scheduling).

Hello, Mark. Thanks a lot for sharing your knowledge!!! Your post has been very useful for me to understand how powerful is EPEI.

I just have a question:

Is there a formula that would include, besides change over and available time, the DESIRED INVENTORY RECOVER for each product to obtain the Rotation Lenght (EPEI)?

Again, thanks a lot for sharing your ideas.

Eli Reyes Reyes

Hi Eli,

Thanks for the question. I am not really sure what you mean by, "DESIRED INVENTORY RECOVER." If you mean that you would like to determine a standard production lot size for each product using EPEI thinking, then you may be heading more in the direction of a triangle kanban using a product specific lot size method. kanban sizing under this method follows the following math: kanban size = average period demand X replenishment lead time (EPEI) X factor of safety. Of course, there's some important math around determining the reorder point (where you physically or virtually place the triangle kanban for replenishment triggering purposes).

I hope this makes sense.

Best regards,

Mark

Hi Mark, just wanted to know your thoughts on this. In one of the Duggan books where they teach interval calculations - I think Creating Flow Through Shared Resources but could be the mixed model one.... don't remember - he shows that to calculate the contribution caused by uptime, he takes the downtime multiplied by the cycle time x demand bar. This doesn't make much sense to me - it makes more sense to multiply the downtime by the total available time and then stack that on top of the cycle time x demand bar. What are your thoughts?

Thanks.