Problem $2$

Consider a sporting goods store that sells golf clubs. The inventory level of these golf clubs is

continuously reviewed. Each time the golf club inventory position drops below the reorder point,

an order is placed with the golf club manufacturer. It costs $$50$ to place an order for clubs. Each

golf club costs $$30\mathrm{.}00,$ is sold for $$45,$ and the inventory holding cost is $$7\mathrm{.}00$ per club per year.

Lead time is $7$ days. It is reasonable to assume that the daily demand for golf clubs is normally

distributed with mean $20$ units and variance $6$ units ${?}^2.$

a$.$ Suppose the sporting goods store has determined an acceptable average time between

stockouts would be $1\mathrm{.}3$ years. Compute the required safety stock and reorder point for an

$(R_{,}Q)$ system. When is an order placed? How many golf clubs are ordered each time an

order is placed?

b$.$ Now suppose the sporting goods store wants the fill rate to be $99\%.$ Compute the required

safety stock and reorder point for an $($R$,$Q$)$ system. When is an order placed? How many

golf clubs are ordered each time an order is placed?