June 10, 2005

Safety Stock

First of all, here's the formula so you don't have to dig through my well-written article for it.

Safety Stock:  {Z*SQRT(Avg. Lead Time*Standard Deviation of Demand^2 + Avg. Demand^2*Standard Deviation of Lead Time^2}

If that wasn't clear to you, I suggest reading on.  This article will explain in detail what safety is used for, and how to use it.

Inventory management is about two things: not running out, and not having too much. Our desire to not run out, along with uncertainties in demand and supplier lead times are why we have inventory in the first place. Essentially, inventory is a reserve system to prevent a stock out. However, as important as it is to prevent such a stock out, we also don’t want to hold onto too much inventory because of holding costs. So how do you balance the two and what is the right amount? More importantly, when should you re-order in order to prevent a stock out? The answer to this can be determined by obtaining and applying the following information about the inventory you wish to manage.

Re-order Point (ROP)

1. What is the average lead time for the part/finished good that you need?

2. What is the standard deviation of that lead time? It is very important to track how long shipments take from you suppliers. If you are not doing this, start. It should be your top priority. Assuming you have tracked the data, excel can very easily help you determine your standard deviation. In excel, go to the toolbar and click on Insert, then click on Function, and choose STDEV and click ok. Then, enter in as much lead time data you have and presto, you have your standard deviation.

3. What is the expected demand you are working with?

4. What is the standard deviation on this demand?  Perhaps this is something you will be familiar with from experience, however, if not, this is something you should be able to squeeze out of Ted from the marketing department.  One way to find it is to look at historical demand and use the STDEV function in excel to determine it.

5. How sure do you want to be that you aren’t going to run out? 90%, 95%, 98%, 99%? Whatever you decide, this will become your service level. Using this percentage, a statistical z-table should be used to get the corresponding “z-value.” A good z-value webpage can be found at http://www.inventoryops.com/safety_stock.htm. So, for example, if you want a 98% service level, you would use 2.05 as your z-value.

Ok, so you’ve gathered this data, now here’s what you do with it.

(Underlined section is safety stock)

Re-order point=Average Lead Time*Average Demand + Z*SQRT(Avg. Lead Time*Standard Deviation of Demand^2 + Avg. Demand^2*Standard Deviation of Lead Time^2)

In this formula, the first term (Average Lead Time*Average Demand) is the average demand.

The second term {Z*SQRT(Avg. Lead Time*Standard Deviation of Demand^2 + Avg. Demand^2*Standard Deviation of Lead Time^2} is the term that allows for the safety stock. In other words, the second term is the optimal safety stock level.

It is not simple to gather all the data that is needed for the calculations. For a product with multiple parts, each part needs to have its own re-order point calculations and its own safety stock calculation. This can all become very confusing if proper computer modeling is not employed.

Although I mentioned excel earlier, excel is probably not sufficient for your company’s software needs. If you have not already done so, it is very important to look into an integrated software package for these calculations and many others.

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Comments

how could we calculate the safety stock exactly? the available equation
safety stock =reorder point -lead time demand
=ROP-Dl

Posted by: anish | Jun 20, 2006 11:11:35 PM

Where can I find a derivation of the safety stock formula? The formula given doesn't seem to cancel out the "days" units.

Posted by: Brad Elhart | Aug 24, 2006 9:23:45 AM

How much of demand variability do you allow to feed into the SS calculation. ie some people like to dampen the amt of demand variability by the average rate of sale. Do you think this is wise?

Posted by: Jason | Dec 18, 2006 5:13:04 PM

Thanks - interesting article, but your formula is inconsistent with other references to this formula within your website.

Will you please let me know which one is correct? (sometimes the average demand is squared and in other references it is not)

Thanks,

Nick

Posted by: Nick | Feb 13, 2007 10:07:13 AM

Thanks - interesting article, but your formula is inconsistent with other references to this formula within your website.

Will you please let me know which one is correct? (sometimes the average demand is squared and in other references it is not)

Thanks,

Nick

Posted by: Nick | Feb 13, 2007 10:19:14 AM

i want how to determine safety stock in hr planning ,i.e.i want to calculate buffer employees in particular process

Posted by: suresh | Apr 12, 2007 2:11:09 AM

In response to Nick's question, average demand is is squared. Here is the proper formula and I apologize for any confusion:

Safety Stock: {Z*SQRT(Avg. Lead Time*Standard Deviation of Demand^2 + Avg. Demand^2*Standard Deviation of Lead Time^2}

Posted by: Charles Atkinson | Apr 13, 2007 12:01:30 PM

Can you tell me how do we arrive at this formaula
Wht is the physical significance of the terms in teh formula??
thnx
dawn

Posted by: dawn | Apr 26, 2007 11:25:31 PM

How do I account for a supplier that is alsways consistently 10 days late? I do not want to change the lead time in MRP because that is his contract obligation, BUT, my standard deviation is at 0.

Any suggestions?

Posted by: LP | Apr 30, 2007 7:55:34 AM

how have you arrived at the formula? could you please explain that?

Posted by: Saket | May 7, 2007 11:15:27 PM

what is the formular for calculating the N value while looking for the utilization rate of a production system?

Posted by: emma | May 9, 2007 5:21:16 AM

Topic is god...but an u come up with some real good practical examples.

Posted by: Avis | Jun 21, 2007 9:38:31 AM

Hi,

On your safety stock function a dimension analysis gives:

Avg. Lead Time*Standard Deviation of Demand^2 = time x 1/time sqrd -> per time

Avg. Demand^2*Standard Deviation of Lead Time^2 = time sqrd x 1/time sqrd -> dimensionless

This gives per time + dimensionless. Shouldn't both be dimensionless?

Ezra

Posted by: Ezra | Jun 26, 2007 12:03:35 PM

Please check for us how to get the figure for reorder sugestion refer to turover demand 12 month , customer back order, Open order as per details example below:

YTD demand :20
Current month (August) :11
Period 1(July):2
Period 2-5 : 0
Period 5-11 : 1
Customer Back Order : 4
Open Order : 2
Stock On Hand : 1

Question is : how i want to do the formula works to get the Suggestion order.

Your early reply is highly appreciated.

Thank You.

Posted by: Zuraidah | Aug 14, 2007 11:23:19 PM

Could you show how you derived the safety stock forumula please? I have tried myself and i'm not sure how you got it

Posted by: gavin | Aug 16, 2007 7:40:20 AM

Safety Stock: {Z*SQRT(Avg. Lead Time*Standard Deviation of Demand^2 + Avg. Demand^2*Standard Deviation of Lead Time^2}

Could you show us the detail meaning?

Posted by: tim | Sep 10, 2007 8:33:23 PM

The article gives a clear picture of EOQ and ROP model, but i feel that it lacks certain level of professional understanding, i would request the author tp come up with more practical examples. The concept of P and Q system can also be included.

Posted by: Mayank | Oct 16, 2007 11:21:06 PM

I'm confuse to determine standard deviation, because i just have data from result of forecast which is all the next demand is the same number, exp: 120 for all 12 months. So, how to determine SS???Urgent!!

Posted by: deen@ | Nov 15, 2007 4:03:47 AM

In the literature it says:

OP = EDDLT + SS
OP = Re-order point
EDDLT = estimated demand during lead lime
SS = Safety Stock

Safety Stock= {Z*SQRT(Avg. Lead Time*Standard Deviation of Demand^2) = Z * Stdev Demand^2 * SQRT(Avg Lead Time)

EDDLT = Avg. Demand*Lead Time

This next term is no where to be found (did you create it by yourself?) --> Avg. Demand^2*Standard Deviation of Lead Time^2

The only thing I don't get is why the SQRT of Avg. Lead Time is taken into account in the calculation of the safety stock.

It's obvious the uncerainty of Lead Time is important by the calculation of the Safety Stock, But why they take (also in literature) the SquareRoot of it?

Kind Regards

Posted by: Alfie | Dec 4, 2007 2:46:22 AM

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