Teddy Bower is an outdoor clothing and accessories chain that purchases a line o

Question

Teddy Bower is an outdoor clothing and accessories chain that purchases a line of parkas at $10 each from its Asian supplier, TeddySports. Unfortunately, at the time of order placement, demand is still uncertain. Teddy Bower forecasts that its demand is normally distributed with mean of 2,100 and standard deviation of 1,200. Teddy Bower sells these parkas at $22 each. Unsold parkas have little salvage value; Teddy Bower simply gives them away to a charity. a) What is the probability this parka turns out to be a “dog”, defined as a product that sells less than half of the forecast (here, forecast is 2,100 units, the mean)? b) How many parkas should Teddy Bower buy from TeddySports to maximize expected profit? c) If Teddy Bower wishes to ensure a 98.5% fill rate, how many parkas should it order? d) If Teddy Bower wishes to ensure a 98.5% in-stock probability, how many parkas should it order? For parts e) through g), assume Teddy Bower orders 3,000 parkas (Q=3,000). e) Evaluate Teddy Bower’s expected profit. f) Evaluate Teddy Bower’s fill rate. g) Evaluate Teddy Bower’s stockout probability.

Explanation / Answer

a)

2100/2= 1050 or fewer units sold.
z=1050-2100/1200 = -.875 or -.88
Value at that point is .1894 or 18.9%
It is probable that Parka would be a dog.

b)

Cu: 22-10=12
Co 10-0=10
Critical Ratio: Cu/(Co+Cu) = 12/(10+12)=.5455
Closest z is 0.12
z=(Q-?)/? 0.12=(Q-2100)/1200
Q= 2244

c)

Z value for .985 is 2.17,
z=(Q-?)/?, 2.17=(Q-2100)/1200,
Q=47044704  

d)

z statistic = (3000-2100)/1200=0.75,
Standard Normal Loss =0.1312
Exp. Lost Sale: 1200*0.1312=157.4,
Exp. Sales: Exp. Demand - Exp. Lost Sales = 2100-157.4=1942.6
Exp. Leftover Inv.: 3000-1942.6=1057.4
Exp. Profit : (22-10)*1942.6 - (10-0)*1057.4 = $12,737

g)

22.7%

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