Example $3$: Safety stock continuous review system $($Q$)$

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?Example $2$: Safety stock continuous review system $($Q$)$

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?