Start with the average demand over a period of time (i. e. a week, month or year). For our example, let’s say it is 20 units per month. Determine the absolute difference between each data point and the average. For example, if monthly demand was 8, 28, 13, 7, 15, 25, 17, 33, 40, 9, 11, and 34 units, the differences from 20 would be: 12, 8, 7, 13, 5, 5, 3, 13, 20, 11, 9, and 14. Square each difference. In our example, this would yield: 144, 64, 49, 169, 25, 25, 9, 169, 400, 121, 81, and 196. Calculate the average of the squares. E. g. 121 Take the square root of the average. This is your standard deviation of demand. E. g. 11
Z-Score of 1 = 84% Z-Score of 1. 28 = 90% Z-Score of 1. 65 = 95% Z-Score of 2. 33 = 99%
Production delays — If your own production process is variable, this may impact the lead time. In addition, the production process of the products you are ordering may vary. Material defects — If you order 10 units and 2 are defective, you will have to wait for the additional 2 units. Delivery delays — Shipping times can be expected to vary slightly at the best of times, and unexpected events like natural disasters or strikes can further delay delivery.
This means if you calculated standard deviation on a monthly basis, and lead time was 2 months, you would multiply the standard deviation by the square root of two. Using our previous example, this means: 11 x √2 = 15. 56. Make sure to convert lead time to the same unit of time measure that you used to determine standard deviation of demand. For example, if you calculated standard deviation on a monthly basis and lead time was 10 days, you would want to convert lead time to . 329 months — i. e. 10 divided by 30. 42 (the average days in a month).
Safety stock = Z-score x √lead time x standard deviation of demand In our example, to avoid stockouts 95% of the time, you would thus need 1. 65 (the Z-score) x √2 (lead time) x 11 (standard deviation of demand) = 25. 67 units of safety stock.
Safety stock = Z-score x standard deviation of lead time x average demand For example, if aiming for a Z-score of 1. 65, with average demand constant at 20 units per month, and lead times over a six month period being 2, 1. 5, 2. 3, 1. 9, 2. 1, and 2. 8 months, then Safety Stock = 1. 65 x . 43 x 20 = 14. 3 units.
Safety stock = Z-score x √[(lead time x standard deviation of demand squared) + (standard deviation of lead time squared x average demand squared)] In our example: safety stock = 1. 65 x √[(2 x 11squared) + (. 43 x 20)squared] = 29. 3 units.
Safety stock = (Z-score x √lead time x standard deviation of demand) + (Z-score x standard deviation of lead time x average demand) In our example: safety stock = 25. 67 + 14. 3 = 39. 97 units.
