Question

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. Due to the long distance and limited capacity, NM must place the order 6 months in advance. A detailed analysis of past data shows that if forecasting 6 months in advance, the number of bags sold can be described by a normal distribution, with mean 150 and standard deviation 60.

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

Option 1: Spain

6 month duration demand analysis:

m	mean	150
s	Std Dev	60
C	Cost	28.5
P	Price	150
V	Salvage	10.4	(10+0.4)
			Formula used
Cu	Cost of under order	121.5	(P-C)
Co	Cost of over order	18.1	(C-V)
CR	Critical ratio	0.8703	(Cu/(Cu+Co)
	So actual order	m+Z*s
		218	NORMINV(CR,m,s)
If	Optimal Order is	218

So profit is 218*121.5 =

26448

For option 2: US

For 3 months demand analysis::

m	mean	150
s	Std Dev	60
C	Cost	35
P	Price	150
V	Salvage	10.4	(10+0.4)
			Formula used
Cu	Cost of under order	115	(P-C)
Co	Cost of over order	24.6	(C-V)
CR	Critical ratio	0.8238	(Cu/(Cu+Co)
	So actual order	m+Z*s
		206	NORMINV(CR,m,s)
If	Optimal Order is	206

SO profit: 206*115=

23666

So in 6 months = 2*23666 =

47332.28

Hence option 2 is better.