Ephemeral Apparel (EA) has been suffering from stockouts of some items and overs

Question

Ephemeral Apparel (EA) has been suffering from stockouts of some
items and overstocks of other items. Robert Michaels, vice president of
marketing, and Michael Roberts, EA’s new vice president of logistics, are
battling over how to set inventory targets for several key product lines
for the 2013 summer season. Orders must be placed in December 2012 to
ensure that products will be available in EA distribution centers by May
2013. Michaels claims that the cost of customer goodwill for stocking
out of any item should be set at two times the selling price of that item.
Further, he claims that because of this high cost of stocking out, the service
target for all items should be a 95% probability of not stocking out in
the season. Roberts says that these are overestimates and will cause EA
to carry too much inventory. Accordingly, Roberts asked the Finance and
Merchandising departments to provide some data to help him develop
service level targets more scientifically. One particular item, for example,
has a projected gross margin (per-unit profit margin divided by per-unitselling price) of 45% and a projected end-of-season salvage value of
20% of the per-unit cost. (Hint: You should be able to express all
relevant
costs in terms of the item’s price, p.)
a. If Logistics VP Roberts accepts Marketing VP Michaels’ estimate of
goodwill cost, what is the best service level for this item?
b. If goodwill cost were estimated at five times the selling price of the
item, what is the best service level for this item?
c. Given these results, what do you believe Mr. Roberts should recommend
to Mr. Michaels regarding his proposed 95% service target?

Explanation / Answer

Goodwill cost = twice he sleling price = 2p where p is the selling price per unit.

Cost price = selling price - profit margin = p - 0.45p = 0.55p

a) Underage cost, Cu = Goodwill cost + profit margin = 2p+0.45p = 2.45p

Overage cost, Co = Cost - Salvage price = 0.55p-0.2p = 0.35p

Optimal service level (CSL) = Cu/(Cu+Co) = 2.45p/(2.45p+0.35p) = 0.875 or 87.5 %

b) Cu = 5p+0.45p = 5.45p

CSL = 5.45/(5.45+0.35) = 0.9397 ~  94 %

c) Mr Roberts should recommend to Mr Michaels that the proposed service target of 95% is very high, and it makes sense when the goodwil cost is more than 5 times the selling price. For goodwill cost equal to twice the selling price, the best service target is 87.5%

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