1. A retail outlet sells holiday decorations for $10 per bag. The cost of the product is $8 per bag. Any units not sold during the selling season can be sold for $5 a bag at the end of the season. Assume that demand for these decorations is normally distributed with a mean of 500 and standard deviation of 100 bags.
a. What is the recommended order quantity?
b. What is the probability that at least some customers will ask to purchase the product after the outlet is sold out?
c. Suppose at the end of the selling season, the decorations have no value and have to be disposed of at a cost of $0.10 per bag. Now what is the optimal order quantity?
d. To keep customers happy and coming back, the owner of the store feels that stock-outs should be avoided. What is the your recommended order quantity if the owner is willing to tolerate only a 0.15 probability of a stock-out?
e. Using your answer to part (d) what is the goodwill cost you are assigning to a stock-out?
2. Ray's Satellite Emporium wishes to determine the best order size for its best-selling satellite dish. Ray has estimated that weekly demand for this model to be 25 units. His cost to carry one unit is $50 per year and the cost of placing an order with his supplier is $25. He's open 52 weeks a year.
If Ray were to use the EOQ method,
a. How many dishes should Ray order each time he places an order?
b. What is the number of times Ray will order this dish each year?
c. How many of this dish will he have on average in inventory?
d. What is the time between one order and the next?
e. What is the annual cost of using the EOQ model for this dish?
f. Ray currently orders in quantities of 50 dishes per order. How much would he save or lose by switching to the EOQ?