Howard Clark is the inventory manager for CrystalClear, an online retailer based in Texas that only sells eco-friendly cleaning products. Cleaning vinegar is one of their most demanded products. Annual demand for cleaning vinegar is normally distributed with a mean of 672 liters and standard deviation of 163 liters. Howard's current inventory policy is ordering 168 liters every 3 months from their main supplier. The lead time between placing and receiving the order is 1 month, and CrystalClear takes ownership of the product as soon as it leaves the supplier's facility. Considering that the cycle service level target is 90%:

Q1: What is the cycle stock (in liters) of cleaning vinegar under this policy? What is the pipeline inventory (in liters) of cleaning vinegar under this policy?

Q2:What is the safety stock (in liters) of cleaning vinegar under this policy?

Q3:Howard knows that inventory performance metrics are closely interrelated, and that once you set up one of them you can imply the value of the other. Considering that the annual holding cost per liter of vinegar is 26 $/liter-year, he wonders what would be the cost per item short (CIS) with his current policy. Could you help him figure it out?

Cost per item short (CIS):

Q4: Finally, Howard would like to explore other inventory management policies. He decides to start by transforming his current policy for cleaning vinegar into a continuous review policy (s,Q). Given that the estimated cost of placing an order is $110:

What should be the new order quantity (EOQ)? What should be the reorder point (s)?