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I am trying to work out the best formula to use for calculating the safety stock to be used in Heijunka/production levelling.

According to this article, the best approach is to use the root mean squared error as the metric for process variation. But it doesn't explore how many multiples of this measure of variation should be used for the appropriate safety quantity. I.e., how does one determine whether one wants to use a safety stock level of 3 times the RMSD, one times, two times, etc? Does it depend on whether the forecast variable is normally distributed? What does it depend on?

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Although I am not familiar with Heijunka method, what I know about standard deviations of normal distributions is that the number of std's away from the mean value represents a probability.

So for example, if you have a weekly demand with mean value of 100, and std of 10, then you can expect that a demand that is:

  • is less that 70 units (-3 stds away from mean) is approximately 0.135% probable
  • is less that 80 units (-2 stds away from mean) is approximately 2.275% probable
  • is less that 90 units (-1 stds away from mean) is approximately 15.865% probable
  • is less that 100 units (0 stds away from mean) is approximately 50% probable
  • is less that 110 units (1 stds away from mean) is approximately 84.135% probable
  • is less that 120 units (2 stds away from mean) is approximately 97.72% probable
  • is less that 130 units (3 stds away from mean) is approximately 99.87% probable

See Normal distribution calculator.

So, you can use as many standard deviations depending on the probability that you want to run out of stock (an equivalent of a statistical significance level).

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This would seem to be a mini-max problem.

  • What is the cost of insufficient stock? This may be low -- a lost sale, or really high, a lost customer, loss of reputation as an 'always got it' supplier.

  • What is the lost opportunity cost of having excess inventory? This is both money tied up in the inventory itself as well as the cost of storage.

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