Problem 1
Consider the following inventory management scenario: Our bottling plant uses approximately 1000 plastic bottles per day (normally distributed), while daily usage has a standard deviation of 70. Order lead time is 2 days (constant).
What is the average demand during lead time for this item?
What is the standard deviation of demand during lead time for this item ?
If I use an order point system, what reorder point (ROP) would result in 100 units of safety stock?
What is the predicted service level using that ROP value?
What ROP value is needed to provide 99% predicted service level? How much safety stock is associated with this policy?
Problem 2
For the plastic bottle inventory problem above, find the amount of safety stock needed to provide service levels of 60%, 70%, 80%, 90%, 95%, 99%, 99.5%, and 99.9%. Prepare a chart that plots the service level (on the vertical axis) as a function of the safety stock level (on the horizontal axis). (This will need to be entered as a scatter-plot or XY chart in Microsoft Excel, since the horizontal axis values are not evenly spaced.) What can you conclude from this chart about the marginal benefit of additional safety stock, as the safety stock level increases?
Problem 3
Consider the plastic bottles demand pattern from question 1. Suppose I plan to instead set up a periodic review inventory system, and I will order this item every 7 days. There is still a 2 day lead time.
The "order up to" level T must cover what protection interval ?
What is the average demand during the protection interval?
What is the standard deviation of demand during the protection interval?
Using this periodic review system, what order up to level (T) would result in 100 units of safety stock?
What is the predicted service level under this safety stock value?
What order up to level is needed to provide 99% predicted service level? How much safety stock is associated with this policy.
Problem 4
Compare the policies found in problems 1 and 3 above.
How does the service level provided by 100 units of safety stock under the reorder point policy compare to the service level provided by 100 units of safety stock under the periodic review policy?
How does the quantity of safety stock required to provide 99% service level under the reorder point system compare to the quantity of safety stock required to provide 99% service level under the periodic review system?
Explain your results for (a) and (b). (Why do we see this difference between the two policies?)