1. Needless Markup (NM), a famous “high end” department store, must decide on th
ID: 334489 • Letter: 1
Question
1. Needless Markup (NM), a famous “high end” department store, must decide on the quantity of a high-priced woman’s handbag to procure in Spain for the coming Christmas season. The unit cost of the handbag to the store is $28.50 and the handbag will sell for $150.00. Any handbags not sold by the end of the season are purchased by a liquidator for $10.00 each. In addition, the store accountants estimate that there is a cost of $0.40 for each dollar tied up in inventory, as this dollar invested elsewhere could have yielded a gross profit. Assume that this cost is attached to unsold bags only.
a) Another supplier in the U.S. offers the same product but at a higher price of $35 due to its higher production cost. For this supplier, NM only needs to place the order 3 months in advance which results in a much better forecast. Past data shows if ordering 3 months in advance, the number of bags sold can be described by a normal distribution, with mean 150 and standard deviation 20. Which supplier should NM choose?
Explanation / Answer
Unit cost, c = $28.50
Selling price, r = $ 150
Salvage value s = $10
Inventory cost, h = 0.40 * 28.50 = $11.40
Understocking cost, Cu = r - c = 150-28.50 = $121.5
Overstocking cost, Co= c+h - s = 28.5 + 11.40 - 10 = $ 29.9
Critial ratio = Cu / (Cu+Co) = 0.8025
Assuming the demand varies between 50 and 250
A = 50
B= 250
Number of bags to be ordered = A + (B-A) * Critical ratio = 50 + 200 * 0.8025 = 160 bags
b)Selling price, r = $ 150
Salvage value s = $10
Inventory cost, h = 0.40 * 28.50/4 = $ 2.85 (You need to hold only for 3 months i.e. 3/12 = 4 , so divided by 4)
Understocking cost, Cu = r - c = 150-35 = $115.5
Overstocking cost, Co= c+h - s = 28.5 + 2.85 - 10 = $21.35
Critial ratio = Cu / (Cu+Co) = 0.8439 , Z = 1.01 for p = 0.8438
Q = Mean + z*std deviation
= 150 + 1.01 * 20 = 170 units
Note - Some of the critical information is missing in part 1. I have shared the response based on information and assumption is taken in the first part.
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