# How do I analyze historical consumption for 13,000 items?

I have data of demands for 13000 SKUs (consumptions from the last 5 years). 6000 of the observations are zeros.  I can’t recognize the distribution of the data . I have tried the q-q plot to find a match to any known distribution. What can I do in this case if I want to find the reorder point? Is it ok to use the reorder point formula which is in your post “Safety Stocks : Beware of Formulas” even though the distribution is not normal?

You do not give a context. Are those SKUs components supplied to a manufacturing company or retail items on supermarket shelves? The demand patterns may be radically different. In retail, for example, the demand for milk is the sum of the quantities bought by a large number of individual consumers acting independently, and the normal distribution is a likely fit. On the other hand, if you are supplying a model-specific part to a car manufacturer, it is unlikely to fit.

Do not try to apply the same approach to all 13,000 SKUs! For example, reorder point makes no senses for the 6,000 items that have had no demand in the past 5 years. You would want to investigate whether they should still be in the catalog and, if so, they are strangers and you need to organize to make or buy them when an order arrives.

For the others, I would suggest you explore the data rather than focus on fitting a distribution, starting with a Runner/Repeater/Stranger analysis. Then, starting with runners, investigate trends and seasonal variations. For repeaters, I would investigate ways to group them into families that make sense for what you are trying to do.

Do not use only the data. In order to understand what is possible, you need to visit the warehouses or distribution centers and understand how physical distribution distribution is organized, and the people involved.

Then consider a range of approaches for different items and item families, including just-in-sequence, Kanban, two-bin, reorder point, vendor-managed inventory, consignment, etc.  Examine how these approaches would have performed with the consumption pattern of the last 5 years. You can also simulate future demand.

# Flow improvements called “5S” at Avanzar | Jeffrey Liker

See on Scoop.itlean manufacturing

“Recently I revisited Avanzar, Toyota’s interior and seating supplier for their San Antonio, Texas truck plant.  Most major suppliers are on-site delivering directly to the factory which in the case of seat assembly is right across a wall. Avanzar’s CEO, Heriberto (Berto) Guerra, was very excited about their Japanese advisor, formerly of Toyota, and all he had been teaching them about real kanban.  I had visited a year earlier and Mr. Guerra was very excited about their Japanese advisor, formerly of Toyota, who was teaching them kanban. A year before that, he said they were making progress in a few model areas and now there was kanban everywhere. Mr. Guerra also raved about the way their advisor was teaching them 5S, which again I found confusing.”

Michel Baudin‘s insight:

A well-documented case of Lean implementation at a just-in-sequence supplier ot seats to Toyota’s plant in San Antonio, TX. An oddity of this case  is that they lump under the “5S” label all sorts of changes that are well beyond it, such as redesigning part presentation at assembly to make frequently used items easily accessible, or kitting parts.

Of course, as long as it works for them, they can call it whatever they want. For communication with the rest of us, however, as Jeffrey found, it is confusing.

# Is the Kanban system to ensure availability of materials or to reduce inventory?

Pranay Nikam, from VCT Consulting India, asked the following question:

“I have designed and implemented the Kanban System at various type of industries. The challenge I face now is not that of explaining people how the system is designed or how it works. But rather clearing the misconception/misunderstandings key industry people have about Kanban.

My understanding of a Kanban System is ‘A Consumption based replenishment system’ with Multiple Re-Order Point (multiple Bins) as opposed to the traditional Two Bin System. In simpler words you keep enough stock to cover for the total lead time and add a buffer for demand variation and supply failures. And keep replenishing the stock as and when you consumes. The replenishment can be through fresh production or withdrawal from Warehouses or procurement from supplier.

Prime objective of the Kanban System is material availability to enable High Mix and low volume production; ultimately to support production levelling instead of running huge batches.

However, some Lean Consultants propagate Kanban as a inventory reduction tool and nothing more than a material scheduling software that can be configured in any ERP Systems.

The Kanban system has many variants, discussed in Chapters 10 to 13 of Lean Logistics. All these variants, however, have the following characteristics in common:

1. They implicitly assume the demand for an item in the immediate future to match the recent past. It is a naive forecast, but hard to beat on intervals that are negligible with respect to what Charlie Fine calls the clockspeed of the business. And the fluctuations are smoothed by leveling/heijunka.
2. They use some form of tokens to signal demand. Whether these tokens are cards or electronic messages, they can be detached from bins and parts and processed separately, in ways that are not possible, for example, in the two-bin system.
3. There is a fixed number of tokens in circulation for each item, which is a key control mechanism for the supply of this item.
4. The protocols for handling these tokens provide unambiguous directions on what should be done. No human judgement call is required to decide which item to move or produce. There are variations where that is not the case, like the French Kanban, which, for this reason, I don’t consider genuine.

The Kanban system  is not just a multiple-bin system, because bins are not used as pull signals. The Kanbans are pulled from bins when you start withdrawing parts from it, which you couldn’t do if the bin itself were used as a signal. If the signals are cards, you can organize them in post-office slots or on boards, which you also couldn’t do with bins. And, of course, you can do much more with electronic signals, which does not necessarily mean you should.

Your description of Kanban omits the goal of keeping inventory as low as you can without causing shortages, and experimenting with the numbers of Kanbans in circulation to test where the limit is, which makes it a tool to drive improvement.

Kanbans work for items consumed in quantities that have small fluctuations around a mean, which means medium-volume/medium mix rather than low-volume/high mix. You use other methods for different demand patterns, like reorder point for bulk supplies, consignment for standard nuts, bolts and washers, or just-in-sequence for option-specific large items… In low-volume/high-mix production you have many items that you cannot afford to keep around and only order from your supplier when you have an order from your customer; it isn’t the way the Kanban system works.

You can do many things with ERP systems but, historically, they have been more effective in managing purchase orders with suppliers than in directing shop floor operations. If you have an ERP system with accurate, detailed data about your shop floor, you can, in principle apply any algorithm you want to produce a schedule. Most ERP systems, however, do not even have structures in their databases to model the behavior of production equipment at a sufficient level of detail, and are not capable of producing actionable schedules. They print recommendations, and the final decision on the work that is actually done is a judgement call by the supervisor, or even sometimes the operator. Within its range of applicability, the Kanban system avoids this with simple rules, by focusing on what is actually observable and controllable at the local level.

So, I suppose the answer to your question is that the Kanban system’s immediate purpose in daily operations  is to assure the availability of materials while reducing inventory, with the longer-term purpose of driving improvement. Pursuing either of these goals at the expense of the other would be easier but not helpful to the business.

# Some Remarks on the History of Kanban | Alexei Zheglov

See on Scoop.itlean manufacturing

“The Kanban method as we know it today has many other influencers and origins besides Ohno and TPS. Two such influencers were of course W. Edwards Deming and Eliyahu Goldratt. Demings 14 Points and the System of Profound Knowledge guide Kanban change agents worldwide. [...] Thus the “watershed” of the Kanban method circa 2013 has many “tributaries” of which the TPS is only one. Those other sources should be studied by those how want to apply the Kanban method effectively as change agents.”

Michel Baudin‘s insight:

It takes nerve to write this sort of things.

Among the tools of TPS, the Kanban system is the only one that has been covered in the media from the beginning to the point of overexposure, because it combines a clever idea with objects you can see and touch.

What some software people did is borrow the names of both Lean and Kanban and apply them to theories with at best a tenuous relationship to the original.

That it worked for them as a marketing technique is to their credit, but I would not advise anyone wanting to learn about the Kanban system to read Deming, Goldratt, or Drucker, who is also referenced.

And TPS is not a “tributary” of the Kanban method. It is the Kanban method that is a tool of TPS, and useful only in the proper context, in conjunction with other tools in a well-thought out implementation.

# Supermarket sizing

Bosch’s Taojie Hua (涛杰 华) asked the following question:

How do you define a maximum limit for a supermarket?
Especially when the customer withdraws less than planned, and the lot can not be formed as a production signal, how can I react to that “deviation” by setting a proper max limit?

The response covers the following topics:

## Supermarkets in Lean

First we have to clarify what we mean by a supermarket in a Lean manufacturing context. As the term has become popular, some plants have started using it for their warehouses, which is clearly excessive. Often, it is used for any kind of buffer on the shop floor, provided it is used to implement pull. I prefer to reserve the term for buffers from which users withdraw items in smaller quantities than are brought in. If pallets come in and go out, I don’t call it a supermarket, but, if 27-bin pallets come in and withdrawals take place 1 bin at a time, I do.

On a shop floor, supermarkets are found on the edges of manufacturing islands containing a group of cells or a production line and contain either incoming or outgoing materials.  A supermarket for incoming materials has more in common with the refrigerator in your kitchen than with the supermarket you buy groceries in. You need one when your plant Materials or Logistics organization is unable to deliver materials in a form that is suitable for direct use at a production work station.

Water spider at Solectron in Mexico (2005)

The supermarket is owned by Production, and more specifically by the first-line manager in charge of the cells or lines it serves. It is replenished  by  Materials or Logistics through periodic milk runs, but parts are withdrawn by experienced members of the production team — cell leaders or water spiders — and move from the supermarket to production on hand carts, gravity flow racks, or by hand. The parts arrive in the supermarkets in bins that are too large for the line side, and leave in kit trays, small bins, or single units.

You need a supermarket for outgoing materials when your production runs are multiples of the quantities needed downstream. This happens, for example, if you only know how to paint parts in batches of 50 with the same color, while assembly alternates colors one unit at a time. In outgoing supermarkets, materials are replenished by Production and withdrawn by Materials/Logistics.

## Supermarket capacity

For incoming supermarkets, replenishment by milk runs is essential because it makes lead times predictable. I am assuming here that the upstream supply chain does not cause shortages. Making it work is no small feat, but this question is specifically on supermarkets. On the withdrawal side, you want to have the smoothest possible consumption rate for all items, so that you don’t have large ups and downs to contend with, which you achieve with  heijunka （平準化)  sequencing of production. Little’s Law then tell you that you have, for means:

$\overline{Quantity\, on\, hand}\left ( Item \right )= \overline{Consumption\, rate}\left ( Item \right )\times \overline{Replenishment\, lead\, time}\left ( Item \right )$

If you take the minimum quantity that Materials can deliver to the supermarket, on the average the Quantity on hand will be half of it. You know the Consumption Rate.  The Replenishment lead time is a multiple of the milk run pitch, plus the time needed for Materials to act on the pull signal, which depends on when the need is identified and how the signal is passed to Materials.

Assume you consume 1 unit every 25 seconds, the milk run pitch is 30 minutes, and Materials delivers in bins of 100 units. You consume 72 parts/pitch = 0.72 bins/pitch. If the milk runs are used to convey pull signals, as happens with the two-bin system or with hardcopy kanbans, replenishment may take up to 2 pitches. In this example, the 2-bin system would cause shortages, but a Kanban loop with two cards wouldn’t, because you pull the card when you withdraw the first unit from the bin and it is still 99% full. If, instead of using cards, you issue an electronic signal when you withdraw the first unit, Materials can act on it in the next milk run, meaning at most 1 pitch later. You still need room for two bins, because the current bin will still hold at least 28 parts when the replacement bin arrives.

In this example, the mismatch between the size of the delivered bins and the consumption rate forces you to hold enough excess material that you don’t need to worry about safety stocks. If it were instead perfectly matched, you could receive a bin of 72 parts like clockwork every 30 minutes, except that fluctuations in consumption occasionally would cause shortages, and you would need some safety stock to protect yourself against it.  Coming up with a sensible plan for any one item in your supermarket is not a major task, but you need such a plan for every item.

The speed with which signals circulate adjusts itself with fluctuations in consumption. The real question is whether your “customer withdrawing less than planned” should be treated as a fluctuation or a permanent drop. In the first case, there is no action required; in the second, you need to recalculate.  In any case, you need to periodically validate the parameters of your pull system to make sure they still reflect reality. In auto parts, it should be done at least quarterly.

For details on pull systems, see Lean Logistics, Part IV, pp. 197-330. See also the two posts on Safety Stocks: Beware of Formulas and Safety Stocks: More about the formula.

# Lean and Kanban: Poker Chips, Kanban and Buffets

See on Scoop.itlean manufacturing

An approach to improving the experience of using a buffet that relies on capping the number of people with concurrent access. It is like the nightclub or museum management system in which a fixed number of visitors is allowed in, and the next one only allowed in when one leaves.

This is in the same spirit as the purely production control approach to Lean, in which you change production planning and scheduling but you don’t redesign the production line itself. For pointers on buffet design, see Waiting For Each Other.

See on www.software-kanban.de

# Hansgrohe uses Kanbans with RFID chips

See on Scoop.itlean manufacturing

“Hansgrohe uses RFID-enabled kanban (signal) cards to track the flow of containers between its two production sites. The company now enjoys several benefits, including accelerated goods receipt and the certainty of having all the required components readily available for assembly.”

The system has been used since 2008, and Hansgrohe provided the following pictures:

The cards look like regular kanbans.

The cards are read when placed in the mailbox on the left.

The full mailbox is read at once.

It should be noted that this system does not eliminate the recirculating cards, but simply replace bar codes with RFID chips as a means of integrating the Kanban system with the company’s ERP system, for the advantages of richer and faster data collection. It does not eliminate the manual handling of cards, at least internally to the plant.

The next step would be to eliminate the cards, attach the RFID tags to part bins, install readers on racks, and implement the replenishment logic electronically. But the readers would have to be substantially smaller than those shown in the pictures.

# Safety Stocks: More about the formula

In a previous post on 2/12/2012, I warned against the blind use of formulas in setting safety stock levels. Since then, it has been the single most popular post in this blog, and commands as many page views today as when it first came out. Among the many comments, I noticed that several readers, when looking at the formula, were disturbed that three of the four parameters under the radical are squared and the other one isn’t, to the point that they assume it to be a mistake. I have even seen an attempt on Wikipedia to “correct that mistake.”

I was myself puzzled by it when I first saw the formula, but it’s no mistake.  The problem is that most references, including Wikipedia,  just provide the formula without any proof or even explanation. The authors just assume that the eyes of inventory managers would glaze over at the hint of any math. If you are willing to take my word that it is mathematically valid, you can skip the math. You don’t have to take my word for it, but then, to settle the discussion, there no alternative to digging into the math.

A side effect of working out the math behind a formula is that it makes you think harder about the assumptions behind it, and therefore its range of applicability, which we do after the proof. If you don’t need the proof, please skip to that section.

# Math prerequisites

As math goes, it is not complicated. It only requires a basic understanding of expected value, variance, and standard deviation, as taught in an introductory course on probability.

In this context, those who have forgotten these concepts can think of them as follows:

1. The expected value E(X) of a random variable X can be viewed, in the broadest sense, as the average of the values it can take, weighted by the probability of each value. It is linear, meaning that, for any two random variables X and Y that have expected values, $E[X+Y] = E[X]+E[Y]$ and, for any number a, $E[a\times X]= a \times E[X]$
2. Its variance $Var(X) = E[X-E(X)]^{2}= E[X^{2} -E(X)^{2}]$ is the expected value of the square of the deviation of individual values of X from its expected value E(X). Variances are additive, but only for uncorrelated variables X and Y that have variances. If  $E[[X-E(X)] \times [Y-E(Y)]]= 0$ then $Var(X+Y) = Var(X)+Var(Y)$
3. Its standard deviation is $\sqrt{Var(X)}$.

# Proof of the Safety Stock Formula

Fasten your seat belts. Here we go:

As stated in the previous post, the formula is:

$S=C\times \sqrt{\mu{_{L}^{}}\times\sigma_{D}^{2}+\mu_{D}^{2} \times \sigma_{L}^{2}}$

Where:

• S is the safety stock you need.
• C  is a coefficient set to guarantee that the probability of a stockout is small enough.
• The other factor, under the radical sign, is the corresponding standard deviation.
• μL and σL are the mean and standard deviations of the time between deliveries.
• μD and σD are the mean and standard deviation rates for the demand.

The quantity under the radical, $\sqrt{\mu{_{L}^{}}\times\sigma_{D}^{2}+\mu_{D}^{2} \times \sigma_{L}^{2}}$ is the standard deviation of the item quantity consumed between deliveries, considering that the time between deliveries varies.

μD and $\sigma_{D}^{2}$ are the mean and variance of the demand per unit time, so that the demand for a period of length T has a mean of $\mu_{D} \times T$, a variance of  $\sigma_{D}^{2} \times T$, and therefore a standard deviation of $\sigma_{D} \times \sqrt{T}$. See below a discussion of the implications of this assumption.

Note that the assumptions are only that these means and variances exist. At this stage, we don’t have to assume more, and particularly not that times between deliveries and demand follow a particular distribution.

If $D(T)$ is the demand during an interval of duration T, since:

$E \left [ \left D( T\right ) \right ] = \mu_{D}\times T$

$Var\left [ \left D( T\right ) \right ]= \sigma_{D}^{2}\times T$

we have:

$E\left [ D\left ( T \right )^{2} \right ]= Var\left [ \left D( T\right ) \right ]+ \left ( E\left [ D\left ( T \right ) \right ]\right )^{2}= \sigma_{D}^{2}\times T + \mu _{D}^{2} \times T^{2}$

If we now allow T to vary, around mean μL with, standard deviation σL , we have:
$E \left [ \left D \right ] = \mu_{D}\times E\left [ T \right ] = \mu_{D}\times\mu_{L}$

$E\left [ D^{2} \right ]= E\left [ E\left [ D\left ( T \right )^{2} \right ] \right ] = \sigma_{D}^{2}\times E\left [ T \right ] + \mu _{D}^{2} \times E\left [ T^{2} \right ]$

and therefore:

$E\left [ D^{2} \right ]= \sigma_{D}^{2}\times \mu _{L} + \mu _{D}^{2} \times \left ( \sigma_{L}^{2}+\mu _{L}^{2} \right )$

That’s how the variance ends up linear in one parameter and quadratic in the other three!

Then:

$Standard Deviation\left [ D \right ]= \sqrt{\mu _{L}\times\sigma_{D}^{2} + \mu _{D}^{2} \times \sigma_{L}^{2} }$

QED.

Note that all of the above argument only requires the means and standard deviations to exist. There is no assumption to this point that the demand or the lead time follow a normal distribution. However, the calculation of the multiplier C used calculate an upper bound for the demand in a period, is based on the assumption that the demand between deliveries is normally distributed.

# Applicability

The assumption that the variance of demand in a period of length T is $\sigma_{D}^{2} \times T$ implies that it is additive, because if  $T = T_{1} + T_{2}$, then $\sigma_{D}^{2} \times T = \sigma_{D}^{2} \times T_{1} + \sigma_{D}^{2} \times T_{2}$.

But this is only true if the demands in periods $T_{1}$ and $T_{2}$ are uncorrelated. For a hot dog stand working during lunch time, this is reasonable: the demands in the intervals between 12:20 and 12:30, and between 12:30 and 12:40 are from different passers by, who make their lunch choices independently.

On the other hand, in a factory, if you make a product in white on day shift and in black on swing shift every day,  then the shift demand for white parts will not meet the assumptions. Within a day, it won’t be proportional to the length of the interval you are considering, and the variances won’t add up. Between days, the assumptions may apply.

More generally, the time periods you are considering must be long with respect to the detailed scheduling decisions you make. If you cycle through your products in a repeating sequence, you have an “Every-Part-Every” interval (EPEI), meaning, for example, that, if your EPEI is 1 week, you have one production run of every product every week.

In a warehouse, product-specific items don’t need replenishment lead times below the EPEI. If you are using an item once a week, you don’t need it delivered twice a day. You may instead receive it once a week, every other week, every three weeks, etc. And the weekly consumption will fluctuate with the size of the production run and with quality losses. Therefore, it is reasonable to assume that its variance will be $\sigma_{D}^{2} \times T$ where T is a multiple of the EPEI, and it can be confirmed through historical data.

You can have replenishment lead times that are less than the EPEI for materials used in multiple products. For example, you could have daily deliveries of a resin used to make hundreds of different injection-molded parts with an EPEI of one week. In this case, the model may be applied to shorter lead times, subject of course to validation from historical data.

# How natural disasters test Lean supply chains

Via Scoop.itlean manufacturing

The floods in Thailand are the latest. Before, there was the Fukushima earthquake and, going back further in time, the Aisin Seiki fire of 1997 in Japan and the Mississippi flood of 1993…   Each time, the press has faulted Lean for making the economic disruptions caused by theses events worse. The actual record is that the vigilance inherent in Lean Logistics and the strength of customer-supplier relationships in a Lean Supply Chain are in fact key to a rapid recovery.

In 1993, Toyota logisticians in Chicago reserved all the trucking available in the area a few days before the flood cut off the rail lines to California, thereby allowing the NUMMI plant to keep working during the flood.

In 1997, when the Aisin Seiki fire deprived Toyota in Japan of its single source of proportioning valves, other suppliers came to the rescue in what the Wall Street Journal a few months later called the business equivalent of an Amish barn raising.

You can, and should protect production against routine fluctuations. That is what tools like Kanbans are countermeasures for. But there is no way you can afford to protect your business against all possible, rare catastrophic events. What you can and must do instead is be vigilant and prepared to respond quickly and creatively to whatever nature or society might throw at you.
Via the Bangkok Post