Periodic Review, Order Up To Level Policy

A given product has an expected demand of 240 units per month, with a standard deviation of 70 units per month. Leadtime is 0.5 months. Customer service level (CSL) has been set so that we have a value of k=1.28.

We want to manage this product's inventory using a (R, S) periodic review policy. We plan to order every 2 months (R = 2 months). Using the k value from above, what is the order up to level, S, for this policy? Give your answer rounded to the closest integer.

Since orders are placed every 2 months, and the demand is variable, the order quantities are not identical. But we can estimate an average order size.

What is the expected average order size for the policy described above?

The product has a lead time of 0.5 months, and a standard deviation in its demand of 70 units per month.

What is the standard deviation of the demand over the lead time and review period? Round to the nearest integer.

How many units do you expect to be short in a replenishment cycle? Give the answer rounded to only one decimal.

How many replenishment cycles are there in a year?

What is the annual cost of the penalty for units short? Round to the closest dollar.