Safety stock is a term used to describe the additional quantities of stock held by a company to mitigate the risk of running out of stock. This therefore acts as a buffer in case the supply and demand are different to what was planned or forecasted. There are many ways in which to calculate safety stock and there are plenty of Safety Stock Formulas available which you could use. Below we will go through 6 different Safety Stock formula definitions to get a comprehensive figure for safety stock. At the end we’ve given you a ‘bonus track’ of EOQ calculation!
Recommend Safety Stock Formula (s):
1. Average SS
Safety stock = (max daily sale per unit * max LT in days) – (average daily sales per unit * average LT)
Although the above safety Stock formula is simple and gives an average amount of Safety Stock the company need to hold per unit of stock however does not take into account seasonal fluctuations (tradegecko, 2010)
2. Heizer and Render (2013)
𝑆𝑎𝑓𝑒𝑡𝑦 𝑠𝑡𝑜𝑐𝑘 = 𝑍𝜎_{𝑑𝐿𝑇}
Z= number of standard normal deviations (Zscore)
𝜎_{𝑑𝐿𝑇} = standard deviation of demand during the lead time.
Although this approach is takes into consideration standard deviation, it does not take account of time by including it as variable in the equation (EmmanuelEbikake, 2015).
3. Greasley (2013)
𝑆𝑎𝑓𝑒𝑡𝑦 𝑠𝑡𝑜𝑐𝑘 = 𝑍 ∗( √𝐿𝑇) ∗ 𝜎_{𝑑}
Z= number of standard deviations from the mean (Zscore)
LT = lead time
𝜎_{𝐷} = standard deviation of demand rate.
On the other hand, this approach takes account of lead time as a variable within the equation. This is one of favourite Safety Stock formula .
4. King method
𝑆𝑎𝑓𝑒𝑡𝑦 𝑠𝑡𝑜𝑐𝑘 = 𝑍 ∗( √ 𝑃𝐶 / 𝑇_{1}) ∗ 𝜎_{𝐷}
Z= Zscore (a statistical figure based on the cycle service level)
PC = performance cycle or total lead time (including transport time)
T_{1} = time increment used for calculating standard deviation of demand
𝜎_{𝐷} = standard deviation of demand
King (2011) safety stock formula, considers variations in demand, lead time, cycle time and fill rate. The purpose of the formula was to overcome the inaccuracies in data on demand. (EmmanuelEbikake, 2015)
5. King (2011)
Safety stock = Z *√ ((PC/ T_{1} * σ_{D} ^{2}) + (σ_{LT} × D_{avg})) ^{2}
Z= Zscore (a statistical figure based on the cycle service level)
PC = performance cycle or total lead time (including transport time)
T_{1} = time increment used for calculating standard deviation of demand
𝜎_{𝐷} = standard deviation of demand
𝜎_{𝑑𝐿𝑇} = standard deviation of demand during the lead time
D_{avg}= average demand
.
This safety stock formula is used when demand and lead time variability are independent and are therefore influenced by different factors whilst still having normally distribution.
But when demand and lead time are not independent of each other, this equation changes to:
Safety stock = (Z *√( PC/ T_{1} * σ_{D}) + ( Z * σ_{LT} * D_{avg})
6 McKinsey & Company Method.
In selecting to consider any safety stock formula, it is important to consider the joint impact of demand and replenishment cycle variability. This can be accomplished by gathering valid samples of data on recent sales volume replenishment cycles. Once the data are gathered, it is possible to determine safety stock requirement using this safety stock formula:
σ_{C }= √R (σS^{2 }) + S^{2 }(σR^{2 })
σ_{C = }Units of safety stock need to satisfy 68 percent of all probabilities (one standard deviation)
R = Average replenishment cycle
σR = Standard deviation of the replenishment cycle
S = Average daily sales
σS = Stanard deviation of daily sales
How to do Economic Order Quantity (EOQ) calculation with examples
The economic order quantity is a method used to calculate when stocks need replenishing, the purpose of this method is to balance the benefits and disadvantages of holding stock, namely minimising the cost of holding stock also mitigating the risks associated with this and reducing the ordering costs, this would then lead to the optimum quantity of goods being kept.
There is one commonly used formula used to:
EOQ= √ (2*C_{O }*D)/C_{H}
C_{o}= Total cost of placing an order
D = Demand
C_{H}= Total cost of holding a unit of stock
In this formula holding costs include:
Working capital costs Storage costs Obsolescence costs

Order costs are calculated using
Cost of placing the order Price discount costs

Below is a worked example (Slack, 2016)
A construction company gets its cement from a single supplier, the demand throughout the year is constant and last year the company sold 4000 tons of cement. After some calculation the cost of placing an order is £50 each time with the annual costs of holding the cement being at 40 % of the purchasing cost. The company purchases the cement at £120 per tonne. How much should the company order at a time?
EOQ= √ (2*C_{O }*D)/C_{H}
EOQ= √(2*50*4,000)/(0.4*120)
EOQ= √(400,000)/(48)
EOQ= 28.87 tons (answer in 2d. p)
Summary:
Like many other statistical theories and mathematical equation, no safety stock formula can be claimed to be best. Similarly no formula can claim to be fit in all scenario. Use your knowledge and experience to find which formula best suits your business.
If you happen to know and used other safety stock formulas please do share in the comments box with me and the supply chain community.
Recommended Book:
Recommended Course:
Supply Chain: Inventory Control & Safety Stock Calculation
I am not sure I can see in your formulae where it is based on the difference between forecast per period (at the cumulative lead time) and the actual demand per period.
I also do not see a safety stock for unreliability of supply which looks ar std dev of lead time and demand over the lead time.
Safety stock shoukd then manage the combination of both of these.
Thus demand safety stock = k*sd(forecast error)*sqr rt(lead time)
k = factor for number of std deviations required for given service level
Supply safety stock = k*std dev lead time
Total safety stock = sqrt( demand safety stock + supply safety stock)
Thank you for the above formulas, I need an help, can we take an example for the each of the above formulas in the real life scenario it would be of great help.
Regards.
Thanks for the formulas. Please advise if we can use minimum sales figures instead of maximum in calculating average SS.