# Safety stock calculation with production forecast variance

I am trying to find an safety stock calculation where the expression incorporates:

• Sales demand variance &
• Production forecast variance

My calculation so far is based on the first two:

$$\text{Safety stock}=Z\sqrt{\left( \frac{PC}{T} \times \sigma_D^2 \right) + (\sigma_{LT} × \mu_D)}$$

where

• $$Z$$ = Z score
• $$PC$$ = Lead time
• $$\sigma_D$$ = Std of sales demand
• $$\sigma_{LT}$$ = Std of lead time
• $$\mu_D$$ = Mean sales demand

I would be very grateful if anyone could sense check this and let me know how historical production forecast error could be included please?

• What do you mean by “production forecast”? Do you mean that the production quantity is random? I.e., if you order Q, you might receive something other than Q? Aug 16 '20 at 20:35
• We work on a push system, so stock is replenished every day i.e. no ordering/reordering. We get an idea of how much stock we can sell for contractual and discretionary sales by way of a forecast. This is of daily granularity but is updated weekly. It also possesses considerable error, which this uncertainty of which, I would like to embed in the SS calculation.
– cmp
Aug 17 '20 at 6:55
• "We get an idea of how much stock we can sell" -- how is this different from demand uncertainty? Aug 18 '20 at 1:12
• Perhaps I should reword that to the amount of stock 'available' to sell. We get an idea of our production one week in advance: i.e. in Week 1 you will have 10 tonnes to sell, in week 2 you will have 20 tonnes. Hopefully this is clear.
– cmp
Aug 18 '20 at 7:01

It might also be possible to merge #1 and 3: If the demand is $$D$$ and the supply is $$S$$, then the random variable of interest is really $$D-S$$, and you might be able to formulate the problem using that r.v. in place of the demand.