So we're using a fixed review period model with base stock $S$, and review period $T$ of 1 month - the period is not chosen optimally to minimise ordering cost like in an EOQ model, it's just a nice round number.
I'm trying to work out how much to order each month. My modelling assumptions are:
- In one month/ review period $T$, $\mu_T$ items are sold, and assuming demand is stochastic, I can calculate a $\sigma_T$
- If that's the demand & std.dev in 1 month, then by the central limit theorem, the demand & std.dev over a leadtime $L$ are given by
- $\mu_{T+L}=\mu_T \cdot (T + L)$
- $\sigma_{T+L}=\sigma_T \cdot \sqrt{T+L}$
Finally, I calculate the base stock $S = \mu_{T+L} + z\cdot \sigma_{T+L}$ where $z$ is some safety factor chosen based on a 95% service level. (see these notes I found, slide 21)
I'm slightly confused why this is. It looks like $S$ is set to cover the demand for 1 period + retrospective demand that happened over the leadtime. Isn't this double counting, I would have expected $\mu_T$, not $\mu_{T+L}$, since each order must be enough to cover the demand between now and the next order, which is $T$ away?
On this graph for example:
It feels like accounting for $L$ would just shift it in time by that much, but the spacing between verticals is still $T$ so surely that's all the demand $S$ needs to account for, not $T+L$
The safety factor makes more sense; every review period must cover its own fluctuations in demand from $\sigma_{T}$ as well as any uncertainty that occurs while the next review period is waiting for its order to arrive.
Can someone provide some intuition? Why is $S$ set that way?
