A retailer for fashion clothes has four seasons. Each season she only has one opportunity to place orders immediately after the fashon show for that season. One of popular lines of clothing in the winter are scarves for men. The seasonal demand for scarves is typically normally distributed with a mean of 1200 and standard deviation of 300. The scarves sell for $125 a piece and cost $60 to source. Unsold scarves at the end of winter geet deep discounted at 50% of original selling price. The contract manufacturer reserves upto 2000 units of capacity for this retailer and no more?
a. What is the underage cost for the retailer per piece?
b. What is the overage cost for the retailer per piece?
c. How many scarves should the retailer order?
d. This year the forecast is for more uncertainty related to the weather and so many retailers for scarves estimate a deeper discount of 80% of original selling price. What is the updated overage cost for these new conditions?
e. This year the forecast is for more uncertainty related to the weather and so many retailers for scarves estimate a deeper discount of 80% of original selling price. What is the updated service level?
f. This year the forecast is for more uncertainty related to the weather and so many retailers for scarves estimate a deeper discount of 80% of original selling price. What is the safety stock for the retailer for this item?
g. This year the forecast is for more uncertainty related to the weather and so many retailers for scarves estimate a deeper discount of 80% of original selling price. What is the new order quantity that is optimal for the retailer?