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?

Answer 1

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.