"That’s not the formula I use" was the start of the debate. So looking at a few refernce books and searching the web here’s what I’ve come up with. How can something so simple have so many variations? Let us count the ways …
1. No. of kanban = (DD*LT+SS*SQRT(LT/TB))/KB+(DD*EPEI)/KB
- Where: DD = Daily demand (units)
- LT = Replenishment leadtime (days)
- SS = Statistically calculated safety stock (units)
- SQRT = Square root
- TB = Time bucket of the safety stock data points (days)
- KB = Quantity per kanban (units)
- EPEI = Supplier’s replenishment interval (days)
2. #KB = (DD*(LT+SS))/KBS +1
- #KB = Number of Kanbans
- DD = Daily Demand
- LT = Lead Time
- SS = Safety Stock
- KBS = Kanban Size
3. Total Req’d Inventory = (Average period demand * Replenishment time) + 1 or 2sigma + safety stock
4. Total Req’d Inventory = (Average period demand * Replenishment time) * 1.X {where X= 20-40%} and the # of bins = TRI / container or bin size
5. # Kanban = ((AD * RT) + (SF * SD))/SCQ
- AD = average period demand
- RT = replenishment time (in the same time bucket as AD)
- SF = the Z factor, typically 1.645 for 95%
- SD = demand standard deviation
- SCQ = the standard container quantity
6. # Kanban = (average demand during lead time + safety stock) / container quantity
7. N = (dL + S)/C
- N = number of kanban
- d = average demand per hour
- L = lead time in hrs
- S = safety
- C = container quantity
8. K=((RT * AC)/Cont) * (SF + C)
- K = number of kanban
- Cont = contents per kanban
- RT = replenishment lead time per kanban
- AC = average consumption per time period
- SF = safety factor
- C = constant, default = 1
The one I use is #5.
I’ve posted a response on this topic on my blog, http://www.leanblog.org or
http://kanban.blogspot.com/2006/08/its-not-formula-that-matters.html
i have a problem with kanban calculation. i have no idea how to figure out the correct solution the following question. if you able to answer this questions, your help will be highly appreaciate. i am the beginner of learning kanban calculation. hope can get your reply soon. your help will be highly appreciate.
.
1. In a lean manufacturing environment a ‘pull’ system is used for material control. This means splitting the day’s production into small transfer batches each controlled with a kanban card.
Consider the time required to process 150 units of a product through four sequential processes with each process taking 2 minutes – use the situation to list and explain the advantages of small transfer batches.
2.
A Kanban system is used to control the manufacture of valves in a feeder cell for a main pump assembly line.
• 2 valves are required to assemble each pump.
• 1850 Pumps are manufactured each day.
• Valve processing time is 0.001days/valve.
• The total authorised inventory for the cell is 5060 and each container holds 253 spools.
• On average a Kanban spends 0.65 days queuing and 0.12 days moving around the system.
How many kanbans are used in the cell?
What factor is being applied to control safety stock in the system?
1. If 150 units are processed in a batch it will take 300 minutes to be worked in the first process, then 300 minutes in the second and so on. The time to process all 150 units through four processes will be 1200 minutes.
If the batch size is one, then it will take eight minutes for the first piece to be processed through all four operations. The last piece will take 308 minutes.
2. Problem states pumps, values, and spools. 2 values per pump. How are spools related to values or pumps?
#K = (AD * R)/C = ((1850 pumps/day * 2 values/pump) * (0.65 days 0.12 days))/253 = 11.26, round up = 12
Safety might be considered the 0.65 days waiting in queue. Maybe don’t need so much.
Thanks Mr Loucka. You information has been very helpful.
In formula 5.
SF = the Z factor, typically 1.28 for 95% <<< I think it should read 90% instead of 95%.
It would be 1.65 times the SD for 95%, ie Z = 1.65 for 95%
and 2.33 for 98% and so on…
Pls correct me if I’m wrong.
Ren, right you are. When looking at customer demand we are interested in protecting from unusually high demand. If demand is less than the average we should have enough stock or in-process to cover. It’s when demand spikes that things get interesting. So we use the one sided normal probability distribution. 95% coverege is the then 50% below the mean and 45% above the mean. So the z-value for 0.05% is 1.645.
[...] listed various formulations of calculating kanban quantities in July 2006. Here are a few more [...]
I’m wondering, most of your examples use the terms # of kanban.
What does 1 kanban correspond to physically? Is it quantities? Cards?
Thanks
Kanban is a card or container of a number of pieces. So “# of Kanban” is the number of cards or containers that are in circulation.
i have a problem of counting number of kanban which is known that :
1. used 12,5% of daily time (1 day = 8 hours working time)
2. daily average production to meet the demand is 2000 units
3. safety stock is 5% of daily average production
4. container capacity is 100 units
would u help me to solve this problem? what is the suitable kanban formula for this problem? i am in urgent!!! thanx a lot.
Jessie,
For kanban think of a container with 100 parts. When the is empty it goes back to the suppler and is a signal to make or buy 100 more parts. Then the container is filled up and returned to the customer. This container makes a loop, going around and around. How long does it take for this one container to make the whole round trip. This we call Replenishment Time. Replenishment Time is not Lead Time.
Equation I use:
Number of Kanban = ((Average Daily Demand * Replenishment Time) + Safety Stock)/Standard Container Quantity
So #Kanban = ((2000 * Replenishment Time) + 100)/100
thanks for the post. its very helpful.
HELP!
This is great information … however I seem to be getting stuck on symantics. I tend to use the formula with standard deviation. If I have an average daily usage of 3.67 parts, a standard deviation of 3.74, a 24 hour replenishment time, and I want to use a z factor of 1.645 … I seem to be getting a kanban of 9.8. The bin can hold 50 parts, but I do not think it makes since to put 50 parts into the bin and my supply can supply whatever quantity I ask for. So how can I tell what my reorder point and quantity should be?
Rick, if your replenishment time is really only one day then why not just use 2 Bins and keep your average daily demand + 2 or 3 standard deviations in each bin.
Also as far as your math goes – your bin quantity of 50 is a variable not a constant! You can make the bin quantity (or what I call Standard Container Quantity any number you want.
So OK, lets do some math … # Kanban = ((AD * R) + (SF * SD))/ SCQ
#K = ((3.67 * 1) + (1.65 * 3.74))/50
#K = 0.19 which doesn’t make sense. If you change SCQ to say 5 then the number of kanban you need is 1.968.
You certain your replenishment time is 24 hours?
This is the situation. I have a drug machine that dispenses drugs to nurses and internal pharmacy that has enough OH stock to refill. The pharmacy has a 24 hour turn around time when the machines warn they are low. The issue is that the low warnings are not set properly and we can run out of drugs. I am trying to optimize the drug machines. Right now we stock the machines with an average of two weeks of stock based on average daily usage … but as you can see, the standard deviation is large. I would like to minimize the stock within these machines while ensuring the nurses have the drugs OH 95% of the time. My idea was to use the Kanban formula to find the right level of stock and the SF to determine the amount of stock needed for a particular Z.
So to summarize:
The machines need to have stock in them when the nurses need the drugs at least 95% of the time.
The pharmacy can refill the machines within 24 hours should the warning system alert them to a low stock level.
I would like to start with the same 2 weeks in the machines and then optimize later. This is because we have 400 drugs in the 25 different machines and do not want to have someone refilling each position every day.
I can set the warning level to whatever I want … the question is, what is that level for the above parameters. I’ll need to do this same process for all machines and all drugs.
From your description it seems that the replenishment time isn’t 24 hours. Semantics – in the kanban calculation replenishment time is the time it takes a card or container to make the complete cycle from empty to full to empty. Imagine say three containers in circulation. An empty container is a signal to refill and return to the point of use. If you put a clock on the container and then follow it through its life you’ll see the full container sitting at point of use, then some parts will be removed, then the container will be empty, and returned to supplier, then refilled, then returned to point of use to sit in queue. In the situation you describe it looks like your replenishment time is 2 weeks plus a couple days.
Perhaps rather than kanban you need to figure out a reorder point, or as you call it “low stock level”. If restocking is truly only 24 hours from warning system alert then you would set your reorder point at AD + (SF* SD) or (3.67 + (1.65 * 3.74)), or 9.84 or rounded up to 10. When stock in the machine falls to 10 you order more.
How much more? Two weeks worth, or something less? You can look into Economic Order Quantity to optimize inventory carrying cost, order filling cost, and service level. Or you can use a fixed order quantity with kanban, but you need to rethink the bin quantity of 50, which I suppose is the quantity that your machine will hold?
Great! Thanks for the help. I came up with the same number and just need to bounce it off of an expert. These drug dispening machines have containers sizes that can be adjusted. Right now they are all set to a size that will acomidate 2 weeks of drugs (based on 6 months of data converted to a 2 week quantity) … therefore the sizes can vary. The order point (low) is set at 1 week, and the critical low point is set at 1/2 of that. My thought was to use the Kanban order quantity of 9.8 and add to that the average usage of 3.67 (times the number of day I what in the machine … two weeks to start). Then optimize by slowly reducing the average number of day OH when everyone feels confortable that the process works.
thoughts?
again thanks for the help!
With a 95% service level there of course will be times when you will be out of stock. People will remember being out of stock but won’t easily be able to judge the frequency. You might want to track a Fill Rate metric.
You might also look at why your standard deviation is so high and if there is anything you can do to dampen or level load. As a rule of thumb I generally avoid kanban when Cv > 1.0 where the Coefficient of Variation is the standard deviation divided by the mean (or average).
Also, demand can change over time, so you will want to regularly recalculate your order points and order quantities.
Good luck!
Rick,
I agree 100% with Lawrence’s recommendations of using a ROP technique, estimating an EOQ, tracking actual stockouts and doing what you can to minimize daily demand variation.
Let’s see if I’ve properly understood your posts so far:
• Lead time = 1 day (24 hours from replenishment signal to replenishment).
• Replenishment interval = your choice; maximum (ROP + ROQ) is limited by dispensing-machine capacity, minimum can be as little as 1 day.
• Target service level = 95% = 1.645 z-value
Perhaps I could ask several more questions about your situation:
• Does each of the 25 dispensing machines hold all 400 different items? Or, does each dispensing machine hold about 16 items, so that 16 * 25 = 400?
• How often do you want the pharmacy to make a replenishment visit to each of the 25 dispensing machines (once per day, twice per week, etc.)?
• Do you have cost estimates for pharmacy replenishment? Cost per trip to the facility that has the 25 dispensing machines? Cost per trip to a dispensing machine? Cost per replenishment of each item in a dispensing machine?
• Is your week (and the pharmacy’s week) a 7-day week?
• Does the pharmacy always replenish within 24 hours? Or is this an expedite-only lead time? If so, what’s the non-expedite lead time?
• What happens during the 5% of the time when a drug is not available for a nurse? Does the drug get expedited immediately?
FYI – with daily average demand = 3.67, and std dev = 3.74, your example item definitely does not have a normal distribution of demand. Instead, it is doubtless right-skewed, and its demand is probably sporadic (some days have no demand). This is important, because your z-value service-level multiplier assumes a normal distribution. When you use a normality-based z-value with a distribution that is right-skewed, you run the risk of substantially understating the safety stock that’s included in the kanban or ROP calculation.
I’ve made some uneducated (and probably wrong) guesses about your example item’s demand distribution, and some other (probably wrong) assumptions, just for the sake of illustration. I ran my guesses through our proprietary safety-stock model, and came up with these example results for your item with average demand = 3.67 and std dev = 3.74:
Replenish once every 14 days: ROP = 53, ROQ = 53, Safety Stock = 0, Avg Qty On Hand = 28.0
Replenish once every 7 days: ROP = 27, ROQ = 27, SS = 0, AQOH = 16.6
Replenish twice per week: ROP = 14, ROQ = 14, SS = 0, AQOH = 11.9
Replenish once every two days: ROP = 10, ROQ = 8, SS = 2, AQOH = 10.7
Replenish once per day: ROP = 12, ROQ = 4, SS = 8, AQOH = 10.7
Notice that with the longer replenishment intervals, ROP = ROQ. This is because the ROQ itself is providing “de facto” safety stock that achieves the 95% target service level with 95% confidence, without additional calculated safety stock in the ROP.
As replenishment interval (RI) gets smaller, two days or less in this example, ROP > ROQ. This is because the ROQ does not provide sufficient “de facto” safety stock, so the ROP must include additional calculated safety stock.
The “de facto” safety stock provided by larger ROQs is not efficient, in terms of inventory performance. That’s why AQOH drops significantly from the 14-day RI to the 7-day RI, and somewhat less significantly from the 7-day to the 3.5-day. However, from the 3.5-day RI to the 2-day RI, AQOH drops very little, and it doesn’t drop at all from the 2-day RI to the 1-day RI. This supports your intuitive conclusion that there’s no value in replenishing every item every day. These AQOH values are an important component of an EOQ calculation.
I’ll be happy to perform our correct, comprehensive safety-stock analysis on up to 30 of your items as a free trial, just as I’ve offered at http://www.resourcesystemsconsulting.com/blog/blog (about the third posting down from the top). Feel free to contact me at http://www.topdownleansystems.com/contact.php.
Also emphasizing Lawrence’s suggestion, you may also be able to correlate demand to predictive factors such as flu season, etc., and adjust ROPs and ROQs accordingly. The more you can do this, the less you need to depend on a static safety-stock level (whether calculated or “de facto”) to achieve your target service level.
David McPhetrige, TopDown Lean Systems
This is a very informative discussion on Kanban quantities.
Can someone help me, how kanban can be used in Made-To-Order kind of scenarios.
Regards,
Vikas.
Even in Made-to-Order there can be lower level items in the Bill of Material that are in frequent demand. In the extreme where you only make a product once and never again then Kanban may be out of the question. Here’s what I do … get usage (demand) history for parts, calculate the daily average and standard deviation. Calculate the SD/Mean (Coefficient of Variation). If Cv is less than 1.0 then maybe you can use kanban to control resupply.
You take the monthly average usage for the item and divide it by 21 shipping days per month. This equals average units shipped per day. Take this figure and times it by the lead-time days it takes to receive the goods from your supplier (the supplier lead-time must be ACCURATE). Always give yourself some cushion here and generally round this number to the nearest case pack. This would be a general rule for ROP.
As far as ROQ it just depends on how many turns per year you are aiming for i.e. if you want 6 turns per year then make your ROQ close to 2 months usage. Remember the ROQ must be equal to or greater than the ROP or you will probably run out of stock at some point in time in the process.
Hi guys,
As i see here is many formulas how tro calculate Kanaban. But which one is the better to choose ?
I’m just a beginner about the calculating Kanban and in fact I don’t know exactly from where to start. Can somebody explain for me the beginning of it?
I will appreciate this a lot.
Viki,
Short answer: The type of kanban calculation you choose depends on your specific situation. Use the simplest technique that achieves your overall business goals. Usually, those goals include sustainability, ease of use, optimal inventory performance and customer-service-level targets. These goals can conflict with each other, so a simple technique may not be optimal when you expand the use of kanban as an inventory-management technique. “Simple” safety-stock calculations, for example, can actually provide suboptimal inventory and financial results, as our white papers discuss at http://topdownleansystems.com/white.htm.
Here are two high-level subjects that may help you choose the right kanban techniques and calculations:
1. Visual vs. electronic
2. Single point of use vs. expanded supply chain
Visual kanban is simplest. See the card at the top of this Webpage. A kanban card shows 1) the item, 2) replenishment quantity, 3) where to get more and 4) point of use. The simplest visual kanban is two-card, with two identical cards.
The simplest kanban-quantity formula determines average usage from when a kanban becomes “empty” until it is replenished and available: Kanban Qty per Card = Avg Usage * Replenishment Time.
Replenishment time is commonly determined by how often you want to replenish, not how long it takes to replenish. It may take only 15 minutes to replenish a kanban from a nearby location. However, you may not want to replenish every 15 minutes, because of significant materials-handling effort. Instead, you may replenish once per day, so replenishment time = 1 day, not 15 minutes.
This simplest application works well when usage variation is minimal, and when shortages can be quickly and easily expedited from a nearby inventory or kanban location (a “supermarket,” stores or warehouse).
As the kanban-managed supply chain expands, the kanban-quantity calculation becomes more complicated, for two reasons:
1. The kanban quantity must include safety stock, since shortages may not be easily expedited.
2. For optimal inventory performance, replenishment time and replenishment interval may need to be different.
Safety stock is an inventory-optimization challenge, since it doesn’t turn over (financially speaking). Kanban with safety stock requires much more complex math. As I mentioned, we have several white papers on optimal safety stock.
Replenishment Time (RT) Different to Replenishment Interval (RI): RT is the time from when a kanban card is “empty” until it is replenished. RI, by contrast, is the time from one replenishment signal to the next. With two-card kanban, RI = RT. However, if you use kanban for external (supplier) or off-site (distribution center) replenishment, RT and RI may be very different. For example, an offshore supplier may have a six-month RT, with monthly releases. So RI = 1 month, and RI < RT. In this example, you would need at least 7 kanban cards, each with a quantity of one month's usage: RT / RI + 1. The 1 "extra" card provides quantity on-hand until the next kanban in the replenishment pipeline arrives. You would likely require more than 7 kanban cards to provide safety stock for usage and/or lead-time variation. Our white papers discuss how to optimize these additional safety-stock kanban cards.
Electronic Kanban: Everyone who has implemented visual kanban has experienced its strengths and weaknesses. Weaknesses include:
1. Cards get lost
2. Cards aren't easily updated
3. Cards are not part of a basic MRP / perpetual-inventory business system, and may require an off-line program or spreadsheet
Due to these weaknesses, many companies use "electronic" kanban. Electronic kanban has two components: 1) Reorder point (ROP) and 2) Reorder quantity (ROQ). These two components can take many different forms, depending on the specific business system. ROP = (Avg Usage * RT) + Safety Stock. ROQ is usually a supplier-established minimum order quantity, a financially-established economic order quantity, a process-driven batch size, or a planning-driven reorder-review interval.
I'll be happy to provide a free-trial kanban optimization analysis on some of your inventory items. I invite you to contact me, at http://topdownleansystems.com/contact.php.
David McPhetrige, TopDown Lean Systems