How do you calculate safety stock using z-score?
Safety stock = (Z-score x √lead time x standard deviation of demand) + (Z-score x standard deviation of lead time x average demand)
In other words, the safety stock is Z-score times the square root of the sum of the squares of the individual variabilities. The previous equations are useful for predicting the safety stock needed to attain a certain cycle service level— a percentage of replenishment cycles.
The safety stock formula is: [maximum daily use x maximum lead time] – [average daily use x average lead time] = safety stock. You can use the safety stock calculator below to calculate your safety stock automatically.
Safety Stock with a Variable Lead Time
As before, "Z" represents the desired service level and "σLT" represents the lead time deviation (see the standard deviation formula for more information on how to calculate those).
A normal distribution chart will show at 90% service level converts to a service factor of 01.28 – this number will represent Z in the equation. σLT: To calculate demand average, you must begin with a certain time frame.
In investing and trading, Z-scores are measures of an instrument's variability and can be used by traders to help determine volatility. The Z-score is sometimes confused with the Altman Z-score, which is calculated using factors taken from a company's financial reports.
“Assuming the normal distribution” (we will address this assumption in moment), the equation for safety stock is SS = Square root(N) x S x NORM. S. INV(F), where SS is safety stock, N is the number of days between reordering, S is standard deviation of daily demand, F is fill rate, and NORM.
Let's say your company sells an average of 10 products per day, and your lead time is about 14 days. However, during peak periods, you sell up to 15 products per day, and delays in inventory shipment mean it takes up to 18 days for products to arrive at your warehouse. This makes your safety stock level 130 units.
Here Z is the service factor that corresponds to your desired service level. To find this figure, you must use a normal distribution chart. To give you an example, for a service level of 90%, the factor would be 1.28; for 95%, it is 1.64; and for 75% it is 0.67.
What Is a Good Z-Score? 0 is used as the mean and indicates average Z-scores. Any positive Z-score is a good, standard score. However, a larger Z-score of around 3 shows strong financial stability and would be considered above the standard score.
What is the z-score for a 97% service level?
| Percentile | z-Score |
|---|---|
| 95 | 1.645 |
| 96 | 1.751 |
| 97 | 1.881 |
| 98 | 2.054 |
If I want to achieve a service level of 98% I just need to look-up what is the Z-factor corresponding to 98%, which is Z = 2.05. Therefore I need a safety stock equivalent to my average demand + 2.05 standard deviations, which is 100 + 2.05*50 = 202.5.
What percentage of inventory should be safety stock? The percentage of inventory that should be safety stock will vary from business to business. For most businesses, about 50% of the average amount of inventory you use during your reorder lead time is a sufficient amount of safety stock.
The minimum safety stock defines the lowest value of safety stock that you want to keep for a material at any given time. It is the lowest allowed quantity of stock that you always want to have available in your warehouse to cover any unforeseen events.
The most common way to value a stock is to compute the company's price-to-earnings (P/E) ratio. The P/E ratio equals the company's stock price divided by its most recently reported earnings per share (EPS).
A z-score measures exactly how many standard deviations above or below the mean a data point is. Here are some important facts about z-scores: A positive z-score says the data point is above average. A negative z-score says the data point is below average.
| Z-Score | Interpretation |
|---|---|
| > 2.99 | Safe Zone – Low Likelihood of Bankruptcy |
| 1.81 to 2.99 | Grey Zone – Moderate Risk of Bankruptcy |
| < 1.81 | Distress Zone – High Likelihood of Bankruptcy |
z = (x – μ) / σ
For example, let's say you have a test score of 190. The test has a mean (μ) of 150 and a standard deviation (σ) of 25. Assuming a normal distribution, your z score would be: z = (x – μ) / σ
The calculation for distribution yields employs the most recent distribution, which may be interest, a special dividend, or a capital gain, and multiplies the payment by 12 to get an annualized total. The annualized total is then divided by the net asset value (NAV) to determine the distribution yield.
To calculate the reorder point in Excel, set up a table as in the image above, and use the formula =SUM(F2+G2) where Column F is your Safety Stock figure and Column G is your Lead Time Demand.
What is the difference between buffer stock and safety stock?
Buffer stock is the amount required to hedge against customer-induced variations, or spikes in demand. It's similar to safety stock. Sometimes it's even called “buffer safety inventory.” But safety stock is the amount required to hedge against supply-induced variations, or shortages in supply.
Safety stock is simply another term for buffer stock, and there's really no difference between them in terms of meaning.
Also known as “buffer stock” or “backup inventory”, safety stock is surplus inventory retailers purchase in addition to their typical cycle stock to mitigate the risk of facing a potential stockout situation.
Safety stock inventory, sometimes called buffer stock, is the level of extra stock that is maintained to mitigate risk of run-out for raw materials or finished goods due to uncertainties in supply or demand.
Using the standard normal curve, the Z- score representing the 85th percentile is 0.67.
