The home appliance department of a large department store is using a lot size–reorder point system to control the replenishment of a particular model of FM table radio. The store sells an average of 10 radios each week. Weekly demand follows a normal distribution with variance 26.

The store pays $20 for each radio, which it sells for $75. Fixed costs of replenishment amount to $28.The accounting department recommends a 20 percent interest rate for the cost of capital. Storage costs amount to 3 percent and breakage to 2 percent of the value of each item.

If a customer demands the radio when it is out of stock, the customer will generally go elsewhere. Loss-of-goodwill costs are estimated to be about $25 per radio. Replenishment lead time is three months.

a. If lot sizes are based on the EOQ formula, what reorder level should be used for the radios?

b. Find the optimal values of (Q, R).

c. Compare the average annual costs of holding, ordering, and stock-out for the policies that you found in parts

(a) and (b).

d. Re-solve the problem using Equations (1) and (2) rather than (1) and (2). What is the effect of including lost sales explicitly?