# (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 $s=190$.