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Managing the right safety stock level, from raw materials to finished goods, is one of the toughest task for organizations around the world. Companies maintain safety stock as a buffer for unforeseen circumstances like demand  variation , delay in shipment due to natural disaster etc., which impacts customer service levels and stock out situations. At the same time safety stock puts pressure on companies financial.

As safety stock is directly linked with the customer service levels, in case of stock out , and companies financials hence organizations should not guess safety stock qty on gut feeling or a hunch but calculate safety stock based on various mathematical algorithms available.

There are three approach to calculate the safety stock

  • Statistical Based Safety Stock
  • Fixed Safety Stock
  • Time Period Based Safety Stock

There are several factors based on which companies should choose the approach which is best suited for them and within the same organization different approach could be adopted per product line or material type .

I would discuss in this blog very basic mathematical models for calculating safety stock based on statistics.  Let us consider a hypothetical scenario to understand it .

Suppose the weekly demand  for biscuits = 100 pallets

Standard deviation of weekly demand = 10 pallets

Standard deviation of lead time = 0

Production Time= 7 days

Production capacity = 500 pallet  per week

Replenishment Time = 1 day

For simplicity consider no variation in lead time and  company is targeting service level = 98 % , which means 2% of time no stock situation arises.

In this case, Safety stock  =  Z × Sqr root (Total Lead Time /Time interval for standard deviation of demand)/× Standard deviation of demand


Here ‘Z’ is a statistical figure also known as standard score.

Tip : It can be calculated by using ‘NORM.S.INV’ in Excel. For 98% service level the value of Z  = 2.053

Z Score.JPG

Therefore , Safety Stock = 2.0534 X Sqr root ((7+1)/7) X 10

                                           = 2.0534 X Sqr root (8/7) X 10

                                           =  21.9~ 22 pallets

Let us now consider another example with no variation in demand but variation in lead time equal to 1 day ~ 0.1428 Week.

Suppose the weekly demand  for biscuits = 100 pallets

Standard deviation of weekly demand = 0 pallets

Standard deviation of lead time = 1 Days

Production Time= 7 days

Production capacity = 500 pallet  per week

Replenishment Time = 1 day

For simplicity consider no variation in demand this time and  company is targeting service level = 98 % .

Safety stock = Z × standard deviation of lead time x Average Demand

                        = 2.0534 x 0.1428 x 100

                        = 29.32 ~ 30 Pallets

Finally let  us consider the scenario which is  closer to real life with both demand and lead time deviations, and they are not dependent on each other.

Suppose the weekly demand  for biscuits = 100 pallets

Standard deviation of weekly demand = 10 pallets

Standard deviation of lead time = 1 Days ~  0.1428 Week

Production Time= 7 days

Production capacity = 500 pallet  per week

Replenishment Time = 1 day

Company is targeting service level = 98 %


Safety stock = Z × √(((Total Lead Time /Time interval for standard deviation of demand)x  (Standard deviation of demand)2) + (standard deviation of lead time x Average Demand)2)

= √(((8/7)x(10)2) +(0.1428 x 100)2)

=  17.83 ~ 18 Pallets  ( Hope I have not made any silly mistake in calculation ๐Ÿ™‚ )

Safety stock based on the above mathematical and statistical base helps the organization to achieve the targeted service level without undue pressure on financials.

In this blog , I have mentioned the basic mathematical formulas to calculate the safety stock based on statistics .  If you are interested to explore more in-depth then there is plenty of material available  on internet with real life mathematical models.


Disclaimer : The views mentioned are my own and  does not represent the thoughts, intentions, plans or strategies of my employer


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