We have now solved the optimal order quantity. When is this order supposed to do? Can we end up in the situation that we have to sell zero stock? In this post we will figure out what is safety stock and why you should have it.

As I told in the previous post, we have to make some assumptions in order to make calculations. Demand is supposed to be constant when we are calculating EOQ. In reality demand seldom is constant. It can vary a lot. That’s why we have to alter our demand in to value for formulas. If we have reliable data in hand we can calculate demand and it’s standard deviation easily. Usually precise calculation of the standard deviation needs a lot of data. Mean demand can be found with much less data. If we don’t have enough data to calculate our standard deviation it can be assumed to follow the Poisson distribution. Then we can use the square root of the mean demand to estimate standard deviation. It gives pretty accurate value of the Poisson distributed standard deviation.

## Standard deviation

- S = Standard deviation
- X
_{a}= Mean demand of the day/week/month

## What is safety stock?

Safety stock is stock that is not meant to be used in normal conditions. If our stock is based on FIFO-principle we can’t define physical safety stock. But when everything is working perfectly we have computed stock amount that we will always have in stock.

Safety stock is meant to cover demand changes and errors. Example if we have delayed delivery, manufacturing errors or demand changes. Safety stock is not easily definable. It is based on service level that is defined by management and is therefore depended on strategy. Costs will increase heavily when trying to get 100 % service level. Defining the service level and safety stock is always balancing between the customer satisfaction and costs.

## Order point

Safety stock is not same as re-order point!

Re-order point should be placed so that delivery time considered we still have safety stock in stock when delivery arrives. We will use safety stock only if delivery is not in time or demand is higher than usual. If we have used our safety stock, used stock should be added in to next order.

## Defining safety stock

We can define our safety stock by demand of the certain period of time, as an percentage of the purchasing lead time or by mathematical formula. First option is easily understandable and safety stock can be easily varied based on seasons.

#### Percentage of the purchasing lead time

This second model is almost same as the first one but is calculated from the purchasing time with the percentage of the particular product. In some products it is acceptable that it can run out of stock so the percentage can be less than 100 % of the lead time.

#### Mathematical formula

Third model is based on safety factor which comes from decided service level. Other variables are standard deviation and acquisition time. This is not very good model is we have season product unless safety stock is computed for every season separately. It is at it’s best on steady demand. In *Factory Physics* by Wallace Hopp safety stock is calculated quite difficulty from re-order point. More general and simpler formula for safety stock goes like this:

A_{s} = KSL^{0,5}

- A
_{s}= Safety stock - K = Normal cumulative distribution function (safety factor)
- S = Standard deviation (example above)
- L = Lead time of purchasing

This formula needs some complicated calculation for safety factor too. This can be easily made in Excel with NORMSINV-formula from the decided service level. Example K = NORMSINV(95%) = 1,644854. (In newer Excel-versions NORM.INV(0,95;0;1)). Notice that in 97,7 % service level our K-factor is 2 and in 99,9 % it’s 3. Pursuit for 100 % service level is extremely expensive because the capital needed for stock. Service level must be defined critically for every product or ABC-categories. As an example in 90 % service level K-factor is only 1,28.

Computer you safety stock here.

If demand and variation is made monthly also Lead time (L) must be in months. This lead time includes all the time that company uses from ordering to shelving. Until the point when product is in shelf ready to be sent for customer.

## Leave a Reply