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I have been studying “Lean Six Sigma for Supply Chain Management” (James Martin) to set up a model to set safety stocks at the right levels. This resulted in (many) questions regarding the method to calculate variance & the resulting safety stock. What I saw studying other sources is that there are many opinions on formulas, that are not necessarily consistent. I also see that very few of the models have been tested…..

I read your articles on safety stock calculation and I like a lot and use in my own models/work: - the lead-time factor is very intuitive - you use both demand variation and forecasting errors as sources (I take the minimum of those 2)

As I have a lot of confidence in your approach, I would like to ask you some questions:

  • Did you do any simulations to verify if the stock recommendations of yr models would actually result in the targeted service levels?
  • You use the mean forecast error σ2 = E[ (yt - y')2 ]. In the formula on excel sheet 2 you use the stdev. Stdev calculates the mean, dividing by n-1. Stdevp would devide by n, which seems more in line with the description of the mean operator E.
  • Dave Piasecki (http://www.inventoryops.com/safety_stock.htm) uses Stdevpa (also based on n) to calculate demand variation vs average. Do you have any thoughts on this?
  • Various people have suggestions/models that calculate a combined variance of lead time + demand. All these models are different. Do you use a(n) (excel)model for this that you trust and are willing to share?
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2 Answers

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About the "normal distribution" assumption, safety stock level is type of "risk measure". Most real distributions (where a social behaviour is involved) are non-normal. A lot of definitions for risk measures exists in literature, some of them dealing with non-normal distributions. For example Expected Shortfall that belong to class of "coherent" risk measures can deal with class of non-normal distributions.

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Can, some moderator remove my first account please. I can't remember how I logged then. – Ross Dec 11 at 9:56
Done. I have removed your previous account. – Joannes Vermorel♦ Dec 11 at 16:50
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Load of good questions.

1) Concerning the stock recommendations, we have both empirical evidence (validated with a few very large european retailers) also strong theoretical evidence supporting the formulas.

Yet, it must be noted that the reorder point formula expressed in our sample Excel spreadsheet is nowhere a definitive answer the question of the optimal reorder point. For example, we are not taking into account

2) and 3) Good points. It would have to be investigated further to check for the fine prints here. Yet, I think the real issue is that actual assumption that the forecast error follows a normal distribution.

Assuming the normal distribution is like making a LARGE approximation, and we have already experimented that if this assumption is good enough to add a lot of value in terms of inventory optimization.

Nonetheless, dividing by n or n-1 is just a minor approximation on top of a much larger approximation, so I guess the actual impact is small.

4) We haven't published so far any model that deal with varying lead time, but it's definitively part of our roadmap. In our experience that are only few retailers that precisely track lead time for every single reorder being made (which should be the starting point of the process) which somehow explain why this did not make it into LSSC v2.

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