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I've been doing a bit of inventory theory, and just wanted to know if I could interpret:

"Tim has decided to keep enough safety stock to prevent a shortage before the delivery arrives during 95 percent of the order cycles.” as “Tim wanting to meet demand 95% of the time”?

Thanks!

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  • $\begingroup$ What is your probability function in the model? Is it normal? $\endgroup$ – A.Omidi Apr 21 at 11:57
  • $\begingroup$ @A.Omidi yes, its normal $\endgroup$ – Anon Apr 21 at 13:09
  • $\begingroup$ Would you mind revising the title of your question to be a bit more descriptive? $\endgroup$ – LarrySnyder610 Apr 22 at 16:18
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I think the two ways of phrasing it are slightly different:

prevent a shortage before the delivery arrives during 95 percent of the order cycles

means that in the long run, there will be a stockout in 5% of the order cycles, whereas

meet demand 95% of the time

is a little ambiguous, but to me it suggests you want to meet 95% of the demands, i.e., stock out for 5% of the demands.

The first measure is the type-1 service level (or cycle service level), while the second is the type-2 service level (or fill rate).

The two are not the same. For example, if you have 1,000,000 demands per order cycle and you stock out on exactly 1 of them per order cycle, then your type-1 SL is 0% (because you have a stockout in every cycle) while your type-2 SL is nearly 100% (because you meet virtually every demand from stock).

The formula that @KevinG included is the safety stock required to meet the type-1 service level (which, it seems, is the service level that the original statement was referring to). But I disagree that the two statements in your original question are equivalent.

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  • $\begingroup$ I remember reading that Type 2 SL was to know the average number of stockouts? Thanks for this! :) $\endgroup$ – Anon Apr 22 at 23:31
  • $\begingroup$ It's 1 minus the average number of stockouts, or really 1 minus the average % of stockouts. $\endgroup$ – LarrySnyder610 Apr 22 at 23:32
  • $\begingroup$ so could we say that for the first statement, we aren't really talking about SL and we're just referring to the probability? $\endgroup$ – Anon Apr 22 at 23:33
  • $\begingroup$ No, they are both probabilities. They are just two different definitions of service level. Both definitions are probabilities. $\endgroup$ – LarrySnyder610 Apr 22 at 23:35
  • $\begingroup$ so just confirming, if in the first statement I used type 1 service level measure that would be correct? $\endgroup$ – Anon Apr 23 at 0:36
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Yes, I believe you can interpret it like this. The term service level describes it well:

Service level is the probability that the amount of inventory on hand during the lead time is sufficient to meet expected demand – that is, the probability that a stockout will not occur. Service Level

Assuming we want to be able to meet 99.9% of the demand would require an disproportionately high safety stock which is not economical for any business.

Relationship between safety stock increase and achieved service level

This exponential relationship comes from the formula

$$SS = Z_\alpha \times \sqrt{L} \times \sigma$$

where $SS$ is the safety stock, $Z_\alpha$ is the inverse of the standard normal distribution for $\alpha$, $L$ is the lead time (in weeks) and $\sigma$ is the cycle service level.

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