I have a question regarding the dimensions of one of the Safety Stock formulas. "D" stands for "Demand" and "LT" for "Lead time". We can assume that Demand is in Quantity per day and Lead time is in days.
$$SS = K\sqrt{\mu(LT)\sigma(D)^2+\mu(D)^2\sigma(LT)^2}$$
Dimensions of the components: $$dim({\mu(LT)}) = time$$ $$dim({sigma(D)^2}) = (Qty/time)^2$$ $$dim({\mu(D)^2}) = (Qty/time)^2$$ $$dim({\sigma(LT)^2}) = time^2$$
First term:
$$time*Qty^2/time^2 = Qty^2/time$$
Second term:
$$Qty^2/time^2*time^2 = Qty^2$$
I am struggling to see how these 2 terms can be added together to yield Qty.
Any help is appreciated. Thanks!
