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446 CHAPTER 10 INVENTORY MODELS

air conditioners over to the following year. Thus, all surplus air conditioners will be sold to a
wholesaler for E50 per unit. Assume that the air conditioner demand follows a normal
probability distribution with ¼ 20 and s ¼ 8.
a. What is the recommended order quantity?
b. What is the probability that Gunnarsson will sell all the units it orders?

16 A retail outlet sells a seasonal product for E10 per unit. The cost of the product is E8 per
unit. All units not sold during the regular season are sold for half the retail price in an end-
of-season clearance sale. Assume that demand for the product is uniformly distributed
between 200 and 800.
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? That is, what is the probability of a stock-out, using your
order quantity in part (a)?
c. To keep customers happy and returning to the store later, the owner feels that stock-
outs should be avoided if at all possible. What is your recommended order quantity if
the owner is willing to tolerate a 0.15 probability of a stock-out?
d. Using your answer to part (c), what is the goodwill cost you are assigning to a stock-out?

17 Isa Distributors, Inc., provides a variety of auto parts to small local garages. Isa
purchases parts from manufacturers according to the EOQ model and then ships the
parts from a regional warehouse direct to its customers. For a particular type of
exhaust, Isa’s EOQ analysis recommends orders with Q* ¼ 25 to satisfy an annual
demand of 200 exhausts. Isa has 250 working days per year, and the lead time
averages 15 days.
a. What is the reorder point if Isa assumes a constant demand rate?
b. Suppose that an analysis of Isa’s exhaust demand shows that the lead-time demand
follows a normal probability distribution with ¼ 12 and s ¼ 2.5. If Isa’s management
can tolerate one stock-out per year, what is the revised reorder point?
c. What is the safety stock for part (b)? If C h ¼ E5/unit/year, what is the extra cost due to
the uncertainty of demand?

18 For Isa Distributors in Problem 17, we were given Q* ¼ 25, D ¼ 200, C h ¼ E5 and a
normal lead-time demand distribution with ¼ 12 and s ¼ 2.5.
a. What is Isa’s reorder point if the firm is willing to tolerate two stock-outs during the year?
b. What is Isa’s reorder point if the firm wants to restrict the probability of a stock-out on
any one cycle to at most 1 per cent?
c. What are the safety stock levels and the annual safety stock costs for the reorder points
found in parts (a) and (b)?
19 A firm uses a one-week periodic review inventory system. A two-day lead time is needed for
any order, and the firm is willing to tolerate an average of one stock-out per year.
a. Using the firm’s service guideline, what is the probability of a stock-out associated with
each replenishment decision?
b. What is the replenishment level if demand during the review period plus lead-time period is
normally distributed with a mean of 60 units and a standard deviation of 12 units?
c. What is the replenishment level if demand during the review period plus lead-time
period is uniformly distributed between 35 and 85 units?
20 The pharmacy department in the local hospital is responsible for ensuring the supply of
drugs and medicines but is also under pressure to control costs. One particular drug
costs E2.95 per unit. The annual holding cost rate is 20 per cent. An order-quantity,
reorder point inventory model currently recommends an order quantity of 300 units per
order.

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