# (s,q) Policy

In this chapter of the book, the $(s,q)$ inventory policy is discussed.

**Summary of discussed problems**:

- Decision rule
- Continuous review
- Period demands (customer order size greater than 1)
- Periodic review (daily review, undershoot)
- Service level
- Backlog at the beginning of a cycle
- Backlog at the end of a cycle
- Numerical examples for gamma distribution, normal distribution, empirical discrete distribution
- Average costs
- Simultaneous optimization of order quantity and reorder point (When is this required?)
- Backorder costs, service level

It is shown that the assumption of continuous review often leads to wrong decisions. For example, consider normally distributed daily demands with $\mu=100$, $\sigma=40$, deterministic replenishment lead $\ell=1$ and a target service level $\beta=95%$. For a given order size $q=200$ under the assumption of continuous review the reorder point is $s=114$. Using this reorder point in a practical situation with periodic (daily) review results in service level as low as $\beta=75%$. The correct reorder point under periodic review is $s=190$.