After an initial peak in demand, the demand for iPhone 6 stabilizes at 3500 units per week

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Question:

After an initial peak in demand, the demand for iPhone 6 stabilizes at 3500 units per week at the Apple store in Jacksonville. The standard deviation of demand is 820 units. The lead time to reorder iPhones is 4 weeks, and the P is 2 weeks. The store manager wants to ensure a service level of 99.5%.

a. What is the safety stock the Apple store has to keep in order to ensure this service level?
b. What is the target inventory for the iPhone?
c. The store does the inventory review today. It has an on-hand inventory of 12,550 units and
there are 7,800 units in the pipeline inventory. How much should they order?

2:

OMEGA, a Swiss watchmaker, has a repair center located in Miami which covers the South East of the USA. The most common service offered by the center is to replace watch bracelets. The demand for this service is 55,000 replacements per year (with a weekly standard deviation of 300 units). The manager of the repair center has to decide how many bracelets he needs to keep on inventory to ensure a service level of 99%. The lead time for receiving the watch bracelets from Switzerland is 5 weeks.

a. What is the safety stock the repair center has to keep in order to ensure this service level?
b. What is the reorder point for the watch bracelets?

3:

This year Amazon offers a new product during the holiday season, natural Christmas trees. In order to avoid stockouts for this new product, Amazon has to carefully plan its safety stock. Based on a market survey, Amazon forecasts a weekly demand of 3700 trees, with a standard deviation of 600 trees. All trees will be shipped to customers from Amazon's distribution center in Kentucky. The lead time to receive the trees from the tree farm located in West Virginia is 2 weeks. Since this is a new product offering, Amazon wants to guarantee a service level of 98%.

a. What is the safety stock Amazon has to keep in order to ensure this service level?
b. What is the reorder point for the Christmas trees?