Kanban

The-Most-Complicated-Formula

Feb 16 2012

Safety Stocks: Beware of Formulas

A formula you find in a book or learn in school is always tempting. It is a “standard.” If you follow it, others are less likely to challenge your results. These results, however, may be worthless unless you take a few precautions. Following are a few guidelines:

  1. Don’t use a formula you know nothing about. Its validity depends on assumptions that may or may not be satisfied. You don’t need to know how to prove the formula, but you need to know its range of applicability.
  2. Examine your data. Don’t just assume they meet the requirements. Examine their summary stats, check for the presence of outliers, generate histograms, scatter plots, time series, etc.
  3. Don’t make up missing data. If you are missing the data you need to estimate a parameter, find what you can infer about the situation from other parameters, by other methods. Do not plug in arbitrary values.
  4. Make your Excel formulas less prone to error by using named ranges rather than cell coordinates. If a formula is even slightly complicated, referring to variables by names like “mean” or “sigma” makes formulas easier to proof-read than with names like “AJ” or “AK.”

The safety stock formula for the reorder point method

Safety stock is a case in point. The literature gives you a formula that is supposed to allow you to set up reorder point loops with just the minimum amount of safety needed to prevent shortages under certain conditions of variability in both your consumption rate and your replenishment lead time. It is a beautiful application of 19th century mathematics but I have never seen it successfully used in manufacturing.

Let us look more closely at what it is so you can judge whether you would want to rely on it. Figure 1 shows you a model of the stock over time when you use the Reorder Point method and both consumption and replenishment lead time vary according to a normal distribution. The amount in stock when the reorder point is crossed should be just sufficient to cover your needs until the replenishment arrives. But since both replenishment lead time and demand vary, you need some safety stock to protect against shortages.

Figure 1. The reorder point inventory model

If your demand is the sum of small quantities from a large number of agents, such as sugar purchases by retail customers in a supermarket, then the demand model makes sense. In  a manufacturing context, there are many situations in which it doesn’t. If you produce in batches, then the demand for a component item will be lumpy: it will be either the quantity required for a batch or nothing. If you use heijunka, it will be so close to constant that you don’t need to worry about its variations.

What about replenishment lead times? If in-plant transportation is by forklifts dispatched like taxis, replenishment lead times cannot be  consistent. On the other hand, if it takes the form of periodic milk runs, then replenishment lead times are fixed at the milk run period or small multiples of it. With external suppliers, the replenishment lead times are much longer, and cannot be controlled as tightly as within the plant, and a safety stock is usually needed.

Let us assume that all the conditions shown in Figure 1 are met. Then there is a formula for calculating safety stock that you can find on Wikipedia or in David Simchi-Levy’s Designing and Managing the Supply Chain (pp. 53-54).  Remember that it is only valid for the Reorder Point method and that it is based on standard deviations of demand and lead time that are not accessible for future operations and rarely easy to estimate on past operations. The formula is as follows:

Where:

  • S is the safety stock you need.
  • C  is a coefficient set to guarantee that the probability of a stockout is small enough. You can think of it a number of standard deviations above the mean item demand needed to protect you against shortages. In terms of Excel built-in functions, C is given by:

C = NORMSINV(Service level)

Service levelC
90.0% 1.28
95.0% 1.64
99.0% 2.33
99.9% 3.09

  • The other factor, under the radical sign, is the corresponding standard deviation.
  • μL and σL are the mean and standard deviations of the lead time.
  • μD and σD are the mean and standard deviation of the demand per unit time, so that the demand for a period of length T has a mean of μD xT and a standard deviation of σDx √T

Case study: Misapplication of the safety stock formula

This formula is occasionally discussed in Manufacturing or Supply Chain Management discussion groups, but I have only ever seen one attempt to use it,  and it was a failure. It was for the supply of components to a factory, and 14 monthly values were available for demand, but only an average for lead times.

The first problem was the distribution of the demand, for which 14 monthly values were available. This is too few for a histogram, but you could plot their cumulative distribution and compare it with that of a normal distribution with the same mean and standard deviation, as in Figure 2. You can tell visually that the actual distribution is much more concentrated in the center than the normal model, which is anything but an obvious fit.  Ignoring such objections, the analyst proceeded to generate a spreadsheet.

Figure 2. Actual versus normal cumulative distribution

The second problem is that he entered the formula incorrectly, which was not easy to see, because of the way it was written in Excel.  The formula in the spreadsheet was as follows:

C*SQRT((AJ4*AL4^2)+(AI4^2*AM4^2))

then, looking at the spreadsheet columns, you found that they were used as follows:

  • AJ  for Standard Deviation of Daily Demand, and
  • AL for Average Replenishment time.

And therefore the first term under the square root sign was σDxμL2 instead of μLxσD2.

The third problem was that the formula requires estimates of standard deviations for both consumption and replenishment lead times, but no data was available on the latter. To make the formula produce numbers, the standard deviations of replenishment lead times was arbitrarily assumed to be 20% of the average.

For all of these reasons, the calculated safety stock values made no sense, but nobody noticed. They caused no shortage, and the “scientific” formula proved that they were the minimum prudent level to maintain.

Sizing safety stocks in practice

There is no universal formula to determine an optimal size of safety stocks. What can often be done is to simulate the operation of a particular replenishment loop under specified rules. For a simulation of a Kanban loop using Excel, see Lean Logistics, pp. 208-213.

No calculation or simulation, however, is a substitute for keeping an eye on what actually happens on the shop floor during production. One approach is to separate the safety stock physically from the regular, operational stock and monitor how often you have to dig into it. If, say, six months go by without you ever needing it, you are probably keeping too much and you cut it in half. With a Kanban loop, you tentatively remove a card from circulation. If no shortage results, then the card was unnecessary. If a shortage occurs, you return the card and look for an opportunity to improve the process so that the card can be removed.

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Feb 8 2012

The Original Kanbans

Via Scoop.it – lean manufacturing

The kanban has met many adventureson its way to becoming a popular tool for the limitation of tasks, projects and works in process. As superhero origin stories go, kanban has an interesting one. As long ago as 8th century Japan, guidelines were set down for the forms and functions of kanban as corporate logos and shop signs. Just as the study of the use and evolution of forms of kanban as an improvement tool is illustrative as to the development of management various industries from manufacturing to software development, an examination of kanban as Japanese shop signs is instructive of the historical and cultural changes that took place.
Read more: Lean Manufacturing Blog, Kaizen Articles and Advice | Gemba Panta Rei
Via www.gembapantarei.com

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Dec 16 2011

How Manufacturing Software Should Adapt to Support Lean Principles

Via Scoop.it – lean manufacturing

This article takes a critical look at the debate between lean manufacturing and MRP software advocates, and how to find middle ground.
Via blog.softwareadvice.com

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kanbancardfromliker

Nov 29 2011

More about Kanbans, and What it Takes to Use Them.

Ever since the world outside of Toyota started noticing its production system in the late 1970s, the Kanban system has received a disproportionate amount of attention compared to other features. It does not mean, however, that it has been accurately implemented in many of the factories that claim to have done it.  To anyone who cared to study it, details have been available in English at least since Robert Hall’s Zero Inventories (1983), the JMA’s Kanban, Just-In-Time at Toyota (1985), Yasuhiro Monden’s Toyota Production System (1993), or an updated treatment in Lean Logistics (2005).

Pressured to implement Kanbans by executives to whom it was little more than a buzzword, many manufacturing professionals found it more expedient to take old, familiar approaches like the two-bin system or reorder-point and call them Kanban. One such system implementing reorder-point through cards placed on a board has become so popular in France that I suggested calling it “French Kanban.” As can be seen in Figure 1, each column on the board is a mirror of the inventory level for an item. Each pocket filled by a card corresponds to an empty slot in stores, so that the remaining amount is visually indicated by the empty pockets on top. The reorder point is crossed when the cards reach the red zone.

Figure 1. French Kanban: Reorder-Point with Cards

Meanwhile, a few academics like J.T. Black at Auburn University or Robert Hall at Indiana University took the trouble to thoroughly investigate the Toyota system as a whole and the Kanban system in particular, but most of their colleagues didn’t, preferring a simplistic rendition of the Kanban system that made their own ideas stand out by contrast. In this context, insisting on the genuine Kanban system is perceived as nitpicking, because the differences are not in the big idea but in the details. You can easily dismiss these details as insignificant until you consider their cumulative effect on thousands of shop floor transactions every day.

Here are two examples, found today in a blog post:

  1. A common misconception is that you pull a Kanban from a bin when it is empty. If this were true, you would just be using a card to implement the Two-Bin system. The Kanban is not pulled when the bin is empty but when you withdraw the first part from the bin, to allow the bin to cover consumption during the replenishment lead time.
  2. Another in the same post was that the eKanban system did not involve physical cards. It is conceivable that, in the future, goods in transit will only be identified by RFID tags, but it is not the state of the art. They still need some form of human-readable identification and routing, for which a purely electronic system would require some kind of screen on each container. In fact, the electronic signal is used only in the return part of the loop, to eliminate the labor-intensive, slow and error-prone handling of unattached cards. On the supplier side, you print single-use cards that are attached to bins for transfer to the customer. When you detach the car on the customer side, you scan its barcode, and this triggers the electronic replenishment signal.

When evaluating or learning a tool like the Kanban system, you have to consider the following:

  1. The objects. They may be cards carrying specific data, bins of particular sizes and configurations, electronic messages of a given structure, … This is what we have to play with. Their physical nature makes a difference, not in a philosophical way but in basic, practical ways. For example, cards can be shuffled and posted on boards but bins cannot. When you send a card, you no longer have it, but when you send an electronic message, you still do. With the former, you have to make sure it doesn’t lose its way; with the latter, that it isn’t accidentally sent multiple times.
  2. The rules. These are protocols for users to follow. They specify who is allowed or required to do what to which objects when. In the Kanban system, the rules say who can issue new Kanbans or remove them from circulation, who attaches Kanbans to bins and detaches them, and what events trigger these actions. The rules give the objects meaning, as the rules of poker do to a deck of cards.
  3. The mapping to reality. This is what happens to materials and goods  in production and logistics when people follow the rules. When applied rigorously in the right context, the Kanban system tells production operators and materials handlers exactly what they should work on. Unlike the traditional dispatch lists, instructions in the form of Kanbans leave no ambiguity and require no judgement call by the leader or supervisor.

Within its range of applicability, the Kanban system is both simple enough for people to apply and sophisticated enough to get the job done. This is a tall order, and we should not underestimate what it takes.

Even in Japanese, the word Kanban has many different meanings, the most common being a sign advertising a store on the street, as you can see by searching Google images for “看板” (Kanban). Figure 2 shows, on a sidewalk,  the Kanban of a beauty salon located on the 2nd floor of the building.

Figure 2. A Kanban in everyday Japanese

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Nov 18 2011

What’s unique about the Kanban system? (Revisited)

10 years ago, I wrote an article by this title in Karen Wilhelm’s Lean Directions, and a detailed treatment of pull systems in Lean Logistics, pp. 199-270 (2005). While 6 to 10 years in an eternity in Information Technology, it is not in Manufacturing, and I have not seen evidence that technological advances since then have invalidated these discussions yet. Also in 2005, Arun Rao and I wrote a paper on RFID Applications in Manufacturing, which outlined ways this technology could be used, among other things, to implement the Kanban replenishment logic on the side of an assembly line. To the best of our knowledge, it still isn’t broadly used, and bar codes are still the state of the art on the shop floor.

For placing orders with suppliers, on the other hand, the recirculating  hardcopy Kanban has never really taken root in the US, and orders are usually placed electronically. When Kanbans are used with suppliers, they are usually single-use cards printed by the supplier to match electronic orders, that are attached to parts and scanned when the corresponding parts are consumed to trigger a reorder. This is the eKanban system, and more a horseless carriage than a car, in that it is an electronic rendition of a system whose logic was constrained by the use of cards.

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Nov 11 2011

Kanban On The Factory Floor

Via Scoop.it – The Kanban system

A software engineer discovers Kanban on the factory floor. http://t.co/FsBxAcbV…
Via blog.timwingfield.com

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