# Inventory Theory

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!

• What is your probability function in the model? Is it normal? Apr 21 '20 at 11:57
• @A.Omidi yes, its normal
– Anon
Apr 21 '20 at 13:09
• Would you mind revising the title of your question to be a bit more descriptive? Apr 22 '20 at 16:18

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.

• I remember reading that Type 2 SL was to know the average number of stockouts? Thanks for this! :)
– Anon
Apr 22 '20 at 23:31
• It's 1 minus the average number of stockouts, or really 1 minus the average % of stockouts. Apr 22 '20 at 23:32
• so could we say that for the first statement, we aren't really talking about SL and we're just referring to the probability?
– Anon
Apr 22 '20 at 23:33
• No, they are both probabilities. They are just two different definitions of service level. Both definitions are probabilities. Apr 22 '20 at 23:35
• so just confirming, if in the first statement I used type 1 service level measure that would be correct?
– Anon
Apr 23 '20 at 0:36

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.

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.